John, Tyler and I have talked about this. I'm 99.9% certain they ferment the dough in half sheet pan quantities (2.5#?) and then, when they get an order for a full pan, they combine two balls.
The high performer might give you something a bit more authentic, but it sounds like, from you and your family's perspective, that the KA AP/high performer blend is going to be tough to beat.
Tyler, I'm not sure about this, but I believe, over time, that L&B, in an effort to save time, went from very thin slices of cheese with full coverage, to the thicker, spaced out slabs you see in the video. I think full coverage is preferable from a textural perspective. Here's a video from an L&B clone/very possible ex-L&B employee:
This is how I'd approach the cheese, going with a slice a tiny bit thicker than the video.
It's a more work, and because you're buying deli mozz, more costly, but I think the end result will be a bit better than the spaced out mozz you see in the L&B video.