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Would it be okay to use the Kreg screw system to build a Tuba HT box? Also, can 3/4" plywood be used and is that overkill to help the rigidity?

Welcome to the forum

Sure, use Kreg screws if you want.
Stick to the plans, and use 1/2" ply. If 3/4" ply was necessary, it would be specified in the plans.
Using anything other than 1/2" ply, from the outset, requires redrawing the plans...

I thought about using those when I set out to build my first T39 sub. I had used them on shelves and things at home. After experimenting with PL glue I realized I needed no screws at all. I bought an electric brad nail gun and never looked back. The brads simple wood the wood in place while the glue cures. As for 3/4 inch ply, its simply not necessary. The designs include bracing and these speakers can take a beating.

If I can figure out how to post a few photos, I will.

The THT is crazy rigid with 1/2", the complex internal structure provides plenty of bracing. No worries

Pocket screws are great, I use them all the time on projects since realizing how easy and useful they are. However, I wouldn't even try with these cabs. I have an 18g brad nailer and a 23g pin nailer. Along with PL and some clamps, you don't need anything more. I especially love the pin nailer since there's no safety and you can quickly secure pieces so they don't move while the adhesive cures. They aren't strong enough as a method to join panels on their own, but with the adhesive they don't need to. I've put biscuits in a few places, but that probably wasn't necessary either. Also, I would think tight spaces would make using the Kreg driver very difficult. I've found that to be an issue even with a right-angle driver and shortened bits on internal angled joints.