Can you flip your plumbing? Giving you the space on the 98" present tub wall for two large vanities since it's a Jack and Jill. Is the shower out past the wall as in the photo? If so you could flip the toilet into that space and add a door and have a private water closet there with door and add more privacy. That's a decent amount of space to allow for some dual use with two users able to use it at the same time with some privacy concerns met. There is a lot of space there to do layouts that would work well for a J&J shared bath.

We have a Jack and Jill bath upstairs and it is divided with the tub and shower area walled off with a door and the vanity with dual sinks in a separate area. That way one can still use the sinks while the other person in in the shower/tub/ toilet area without tying up the entire bathroom for the other person.

I have a tub on a pedestal or plinth as some call it and I don't have any cleaning issues with it. It's 68" which is plenty long enough, it could be shorter actually since I'm only 5'4". My faucet is the British telephone type that hangs up on it's stand. It has it's floor mounted water supply. That was an expensive faucet even with going cheap with an off brand it was still over $800 and if I had gotten a name brand it would have been more than $2000 for it all. I found that the spout and two faucets with spray was one thing but then they have to add in all the components of the chrome pipes to the floor and I don't know what all before it was all said and done. Sort of like when you buy the washer and they need to add for the hoses etc. It still wasn't a deal breaker. I ended up buying a Victoria + Albert "York" model tub and I love it. I"m so glad I ripped out that horrid jetted gigantic tub. I have never looked back on that decision. We never used it and ti took up so much space. It had gunk in the jets from day one and I couldn't get past it no matter how much I cleaned it the black gunk still came out. You did well to rid yourself of that space hogging tub. Well done!

"How much space should I leave between the tub and the long/back wall?"

Try for a minimum of 4" between the tub and any adjacent surface.

"Should the faucet be on the long wall or one of the short ends? What type of faucet is best?"

Many people prefer the plumbing to be on the long side of a symmetrical tub, that allows the bather to sit with their head at either end of the tub. If the tub has a "head" and a "foot" end, then the plumbing will usually go on the long side of the foot end. I can't recommend any particular manufacturer.

"The custom vanity (width to be determined) is on a 66" wall perpendicular to the tub. I was thinking about putting a cabinet next to vanity at the foot of tub. Does this sound like a good plan? Who should I design the cabinet?"

That can work, as it'll give some storage for the person in the tub. Perhaps a shelf for candles, a towel, etc. Based on the dimensions of the cabinet you could have some of the upper/lower storage in the cabinet facing the vanity and some facing the tub.

"How much space should I leave between tub and the short wall? The built in cabinet?"

Same, 4" minimum.

"Any advice about a cabinet size? "

Depends. You can have a floor-to-ceiling cabinet that will enclose the tub in an alcove. Lower storage in that vanity can face the sink, some of the upper storage can face the sink and some on the end of the cabinet can face the tub, just like the end faces the rub in your inspiration photo.