I had the same concern when I installed two fans and track lights in a long room. My room, however has a flat ceiling. I used essentially your method, mounted the fans on the centerline of the room and the tracks parallel to that centerline, with the lamps placed so that the blades wouldn't block the light. However, I had the advantage that I could temporarily mount the tracks and experiment. Where did you get your angles alpha and beta? Since you propose gimbal mounted lamps, you could adjust the angle of the strobe effect is too great (the angles provided by WAC aren't exact because the illumination cone doesn't have a hard edge). You could always shorten the downrod to raise the fan. Your dimensions j and k on the side view don't appear on your top view (they look like they should be the same as g and i on the top view, but they're not).

Are you going to install these yourself? If you are, you will have more "wiggle room".

Thanks, @mtvhike, for your note.

The angle alpha (α) I got using trigonometric ratios. Arc tangent function on the two legs of a right triangle (possible because I know the room's width, and I tape measured the highest point and lowest point of the vaulted ceiling).

The angle beta (β) is supplied by the manufacturer of the light. The 6" WAC gimbal has a 45 degree angle. (Interesting; I did not know that WAC's angle data is to be read as 'approximate'. Thanks!)

Dimension "a" on the top view should also be "a" on the side view. "G" on the top view should match "k" on the sideways view. "J" on the side view should match "i" on the top view. (As I'm writing this, I realize that doing a mirror image reflection of the sideways view might have made this easier to visualize. Sorry; my mistake.)

Unfortunately, I'm not confident enough in my electrical ability to want to do the wiring/mounting myself. Maybe some day -- on an easier project.

The ceiling is > 16 feet high at its highest point, and there won't be too much room for experimentation. I wonder if there's software or a better method/software so that our electrician could "measure twice; cut once."

When I said "approximate", I was referring to the fact that the edge of the cone of light is not sharp. It's like the penumbra in a solar eclipse, in that the edge of the shadow is blurry. Is "k" in the side view the same as "g" in the top view? As an experimentalist, I always like to check theory with actual measurements, if possible. If you got one of the WAC lights and wired it up to an extension cord and shined it on a wall, you could measure how blurry the edge is.

Thanks @mtvhike for clarifying. Sorry for misinterpreting.

To your question: "K" on the side view = "G" on the top view.

I've got to wonder if there's software or an easy method that makes this easier.

We have a master bedroom roughly the same size, 9' ceilings with a tray, no vault. Definitely do a center fan with light and hanging (low) as per your drawing, it won't draw air properly unless it is a fair distance below the ceiling. Make sure the fan/light has a remote control and hang it on the headboard of the bed for fan adjustments during the night (experience here). To get the 'layers' of light they recommend, place 8 (or more) can lights around the perimeter of the ceiling, 2 on each side about 18" in. They will be far enough away from the fan that there will be no strobing. No need here for high-lumen floodlights or gimbal fixtures as per your plan, 4 inch 500 lumen fixtures will be fine, they will give a medium level of general lighting around the perimeter without blinding one's eyes, I would definitely go with pancake LED fixtures. For individual control of the two fixtures over the headboard, wire them to individual L & R wall dimmer switches placed on each side within an arm reach from the bed.

Thanks, @formulaross20

How did you arrive at this placement (18" out from ceiling for a flat ceiling 9' tall)? Draw it out? Experiment with placement (like @mtvhike until it was perfect)? Bring in an excellent lighting consultant? Is your fan a 54"?

Curious why you're advising against gimbals. With a vaulted ceiling set at 30 degrees, the electricians who visited said we'd end up with oddly angled lights (not down) unless we used fish eye or gimbal fixtures (or put the lights somewhere other than the ceiling).

I'm hoping that a dimmer switch on the led gimbal wafers will give us tons of control on luminosity.

Gimbals are not meant to be used as downlights. They produce incredible glare as the light source is not obscured and they need to have spot beams. In a vaulted ceiling use an adjustable can with slope trims. For instance Juno IC4AL with 48LCWH trim. Most makers offer such a thing. You will want to use a narrower beam on the higher part of the ceiling and possibly a brighter lumen package.

I don’t like recessed lights for general illumination, particularly in bedrooms. They cause unpleasant shadows, and make the ceiling dark. Vaulted ceilings are a great match with uplighting - this can be done with cove lighting or sconces. Another option would be monorail suspended to the same height as the fan. Adds a great deal of flexibility - you can aim the heads where the light Is needed.

Good point on the gimbals and the sloped ceiling; I had my flat ceiling in mind as I wrote.

How did I arrive at 18"out from the wall. Easy, the tray ceiling started upward at about 24" out, and I didn't want them up against the wall. 18" was about right.

Thanks, @nexp and @formulaross20 for your helpful comments. It's giving me lots to think about. Appreciate it!

@nexp -

The vaulted ceiling is right against the roof. The electricians were concerned about not having space and not knowing where the joists sit.

The leds on the gimbal sit in a conical 'housing' (see picture below). Does this not cut down on glare and provide some directionality? The well-regarded lighting supply store where we live said something to that effect.

Some electricians did recommend sconces. Our concern had been that we couldn't get the 12x12 - 13 x 13' room (with 16' ceiling at highest point) bright enough without covering the wall with sconces. We also came to the conclusion that we couldn't agree on a sconce design and didn't want lights that drew attention to themselves. For better or worse, that was our reasoning process.

Was unfamiliar with cover lighting. Unless I'm misunderstanding, that option requires either a new build or adding drywall in which the cove lighting sits (like this picture: https://cdnassets.hw.net/dims4/GG/2e40252/2147483647/resize/876x%3E/quality/90/?url=https%3A%2F%2Fcdnassets.hw.net%2Fd8%2F3c%2F7a47c1db4b85aa02bb66b0777ac8%2Flinear-flourescent-source-tcm47-2193613.jpg). Forgive me if I'm misunderstanding.

Monorail is a very interesting suggestion. I think one electrician mentioned something similar "suspended track lighting". I kind of like this idea. If I'm remembering correctly, my wife did not. She said it would make the room look really "busy" to add both a monorail and a fan (the fan we really need for hot/humid southern months in the DC metro area -- otherwise, we'd prefer not to have it at all from an aesthetics perspective).

The gimbal will not really reduce glare. They will be extremely bright, concentrated points of light when on. The specs don't detail how much adjustment they allow, so I can't tell if they would even point straight down in a 30 degree ceiling. To avoid glare in a recessed light, you need the light source to be deeply recessed, and a reflector that will not be bright (it sounds counter-intuitive, but a clear reflector cone does not appear bright like a white baffle does).

Not all cove-lighting requires building a cove - some products are finished sheet-metal and designed to be exposed. Here's an example: https://www.solidstateluminaires.com/products/createacove/

You certainly wouldn't need to :"cover the wall with sconces" if you use high-output sconces designed for uplighting. With decorative sconces, certainly. You could fully light the room with 4 sconces such as these: http://belfer.com/products/sconces/ws-7230-led-120v/

If you go with recessed lights or sconces, do remember that the taller half of the ceiling is 6ft higher than the lower half. If you're shining light down or reflecting light off of it, the fixtures on the tall part should have a tighter beam spread and possibly either a different lumen package or be on a separate dimmer so that the brightness appear similar. Given the same beam spread, a recessed light 6 ft higher will have a beam diameter about 3 times larger and center-beam brightness about 1/6 as bright.

Monorail is certainly a bit more visually intrusive. If it hangs at 9ft off the ground (level with the ceiling fan) it probably wouldn't be all that intrusive - you wouldn't see it unless you were actually looking up. If you go that route, it should be no more than 2ft from the perimeter walls. Tech and PureEdge are the two common makers of it.

Thanks @nexp for clarifying.

Now I know a lot more about cove lighting and monorail. Didn't realize there were ultra bright sconces.