@rwillett glad for you to join the club of cabinet builders 🙂.
We met at the SW bash (I played your EMG loaded Strat). Sadly I left my BC112mk3 in the car to save space but had I known you were interested in what someone with two left thumbs can do I would have brought it out to show you.
For the braces in the same direction, there is actually some theory involved around standing waves: you want the brace gaps to not be equal to each other, else you encourage standing wave resonances. Saying that, there's a joke Q: What's the difference between theory in practice? A: In theory they're the same but in practice they're different. For a cabinet of sizes we're talking about I wouldn't be able to hear a difference, but you may have more sensitive ears.
On the subject of wadding, again I don't think I could hear a difference at gigs, but that may just be because I forgot to remove the wadding in my ear canal. If you're a weight weenie and are considering putting holes in braces to shave grams off there, no-wadding would be much easier.