case it out like a doorway

We have another opening about 10 feet away from this one, which means I'd have to case that one too.

I like the openings being uncased; is there any other way to do it? Would it be improper to get a new piece of trim and cut the bottom to fit the floor such that the tops of the trim were uniform/level across the two different floors?

Even if we did case the opening, there would be a left-over problem to deal with: there would be a gap between the top of the carpet and the bottom of the casing, as the carpet sits lower than the tile. Not sure how to deal with that.

Install a continuous single piece and undercut the side where the floor is high or add a piece to the bottom of the side where the carpet is low. Or you could install a single piece and shim the carpet where it meets the tile to eliminate the gap under the base.

Johnson Flooring Co Inc,

So far, it seems like the easiest solution would be what you said: undercut the side where the floor is high. There's about 10 feet of the trim to the right of this transition, so I'd be undercutting that much trim, which would be obvious when comparing the two rooms, but there will be a large shelf against the wall, covering almost all this trim. I don't like the idea of shimming the carpet; that may be too obvious to tolerate.

G & S Floor Service, we did such short trim because our ceilings are 7 feet, and we didn't want the floor trim to be visually overwhelming with such a short ceiling.

Our openings are uncased; if we do decide to case them without changing the current floor trim (which is used in every room in the house), do the casings need to match with the floor trim?

Is it proper to cut the cased opening at the bottom to fit the floor, as in this example:

Casings should be inviting, since it's a passageway to another area. It doesn't necessarily need to match the baseboards. But in your case, it's probably the best thing to do. If, you use wide casings, it would overpower your baseboards.

Finishing around casings: undercutting the casing and installing the flooring under it will give you a clean look. And it is much easier to do than to scribe flooring to a casing profile. Thresholds and transitions should butt tight up to the face, just as shown in the image.

You will have a difficult time mitering those corners on a continuous piece at different heights.