wouldn't adding two highly regarded subs bring them to the same full range sound as the floorstanders under consideration. Or is it about the crossover and coherence of the sound coming from a transducer housed in the same cabinet?
This is only my opinion FWIW, but I’d say no to the first and yes to the second. Adding two subs to your Tylers would yield substantially better bass that the LSAs can produce and probably do nice things expanding your soundstage as well. And if LSA succeeded in capturing some of the magic of the Joseph Audio crossover, and it seems like maybe they have from what I’ve read in the reviews, then that benefit you’d only get with the LSAs. I know Tyler makes very good speakers so if you’re happy with their sound there’s a very good argument to be made to just add a couple good subs.
I guess if I was you and just to be sure I’d try a pair of the LSAs and chalk the 10% restocking fee (if you return them) up to getting better peace of mind you made the right choice. It’s really the only way to know for sure. I tend to doubt the Statements are all that much better than the Signatures, but it’s also not like the Statements are all that expensive at their sale price. Anyway, that’s all I got and hope it helps somewhat.