Here's the easiest, or should I write an easy solution, hopefully in words and terms that you can understand. And hopefully within your budget. Symmons makes a very good pressure-balanced valve, the Temptrol line. They sell them at Home depot for around $90 give or take, depending on what comes with the valve. They may sell the valve alone, I'm not certain. I've usually seen it packaged with a shower head and tub faucet. I'm not terribly familiar with big box plumbing. If they don't sell the valve alone, you'll want a "basic valve kit" that comes with a pressure-balancing valve with a built-in tub/showerhead diverter lever, a faucet spigot, and a shower head. They make a few variations of this, but it's general designation is "96-2". Although it comes with a shower head, you can buy your own handheld hose and head to attach to the arm that comes out of the wall. Or if they do sell just the valve by itself, buy the valve, plus a tub spigot, plus a handheld outlet, a handheld hose, and a handheld head. Yes, there are variables because you're asking for a slightly non-standard set-up. Then you want a second Symmons Temptrol valve. If you can't buy just the valve, buy the 96-1 valve kit, which is the same valve as above but it just includes the shower head. No tub spigot. That will feed the rainshower head which you'll have to purchase on your own. Although the valve still has the diverter lever, when it's plumbed to just a shower head, in this case a rain head, the diverter lever will act as a volume control to the rainhead instead of a diverter to the tub. You'll have a hot and cold water supply line coming into your shower. Split both lines with a copper "T" fitting so you have two hot water and two cold water lines, one to feed each Symmons valve. The 96-2 valve will feed either your tub or the handheld. You choose which with the diverter lever built in to the valve. That's your typical bathtub/shower setup. The separate 96-1 valve will just feed the rainshower head. Two different controllers, but it keeps thing simple and affordable. Plus you now have the ability to select different temperatures for the two shower heads. There are other ways to do this, but I'm trying to keep this simple and inexpensive for you. Symmons does sell valve kits that have all the goodies you want, but they can get expensive, up in the $500-$800 range, but they don't allow the two shower heads to be used at the same time.

Omg, lol, engineerchic! I was thinking as I read your post that I had the same thing happen to me with Kohler, then read it was even the same line! I loved that stacked thermostatic valve set though. My very experienced plumber was completely confused by the diagrams in the instructions. Seems to install it for a normal arrangement of single handheld shower head and tub spout is not what they intended! After several days with no shower due to this stupid valve issue we returned it all and got a Price Pfister set locally that looks just as nice and was about $1,100 less. So much for splurging on good fixtures, we saved enough for all the "extras" that went in the room outside the fixtures! And looking back, the most entertaining part was the confused look on the plumbing guys at HD when I insisted they reassure me all the valves that are needed for the rough in are included in the box. That was all separate, and very expensive, with the Bancroft line. They were completely taken aback that you can even buy a trim kit without a rough in valve, but I assured them that yes, that was absolutely possible, and I had done just that. They thought I was nuts.

I can't get the photo to show up but it sounds from the link that you ultimately want to have a shower head, a hand shower, and a tub spout. We just did this. Here is a non professional explanation (so take it with a big grain of salt!). I relied of a plumbing person to ensure we got all the various pieces we needed for inside the wall, and we used one knob that did water temperature and volume, and then another knob that determines where the water comes out (it's a five way Diverter, so we can do spout, spout and shower, shower, shower and handheld, handheld). I am not using the correct terms for these devices, sorry. I think there are two choices for the temp/volume device, depending upon ihow you want to do that (ours is two dials stacked on top of each other, one is volume, other is temp). But there are other ways to do that part. You can get any brand of valve trim you like, as long as it coordinates with what mechanisms are inside the wall (we have Grohe hand shower and shower, delta valves and a Delta spout, sounds awful but we liked the appearance of those pieces). Hope that helps a little!

Instructions: https://www.thespruce.com/installing-toilet-closet-flange-1822506. As instructed, you have to figure out the type of spout, slip-on or threaded. Sample (Delta U1072-PK) replacement spout with diverter for hand shower. This particular spout can be used both threaded or slip-on (see Installation Guide linked to web page).