This isn't really an answer, but here are a couple of links that are vaguely related to glider syntheses via LLS:
TigerCub414's first foray into glider synthesis
my brief experiments with LLS, which included at least one round of expanding-ring predecessor searches, which tried to guarantee stable stuff in the center (you can definitely do that in LLS with variables, then hard-code whatever the stable stuff is once it has settled.)
I didn't have a good way of biasing the expanding active ring to look like a lot of colliding gliders. That seems to be the hugely unworkable part of this problem of getting glider syntheses out of LLS, or any predecessor-hunting algorithm.