Sounds like a cool project, probably more suited to the hobby CNC subreddit: /r/hobbycnc , but I'm still happy to throw in my 2 cents here.
Instead of building up trucks with threaded rod / bearings / nuts, and using an aluminum tube for your linear motion, I would highly recommend using off the shelf linear bearings and shafting. The proliferation of the hobbyist DIY CNC / 3D Printer segment has flooded the market with cheap linear motion components. It's still going to be a bit more than your proposed solution, but I think it would be worth it - you'll save yourself a lot of frustration and end up with a better performing solution, even using the cheapest off the shelf components. Something like these, for example:
For the gear rack / spur gear: Do the individual "blocks" the louvers are attached to need to move independently of each other, or can they all move ganged? I'm assuming you need the independent linear motion, but just in case you don't, it would be much cheaper to use one motor to turn a single leadscrew that runs the full length of the machine axially and have a nut on each "block".
Assuming you need the independent linear movement, your use of a gear rack is a good solution. You mentioned wanting to use NEMA17 motors but were unable to locate a gear that would fit on the 5mm shaft. McMaster has brass spur gears with the DP and PA to match your rack with a .1875" bore, however they're brass, not stainless:
You'd obviously have to ream the bore to fit a 5mm shaft, but that shouldn't be much of an issue. If you can't live with brass, and you can't find a 32DP 20° spur gear with an appropriate bore elsewhere, you could always turn down a bushing to press fit on the 5mm motor shaft to make the larger bore spur gear work. If you're not paying for your time to make the bushings, the material cost for that is going to be a lot less than the price delta between the NEMA17 and NEMA23 steppers.
Also, if the "blocks" are moving independently of each other, you probably want to put limit switches on them to prevent them from running into each other and trashing your steppers / gears / whatever else.
Lastly, I'd try to avoid using the 2x2 wood stud for that structural component. Structural timber like that is terribly unstable and not dimensionally accurate at all, I can see it causing you issues - take a look at 80/20 aluminum extrusions for those structural components. They're obviously more expensive than wood, but you can find good deals on eBay (the actual manufacturer of 80/20 even has an eBay store where they sell surplus / off cuts / scratch & dent / etc.: 8020-Inc-Garage-Sale)
Anyway, hope some of that is helpful. Like I said, looks like a cool project, and I think it's certainly achievable, even without taking any of my suggestions on board. Oh, and BTW - nice looking rendering you made there!