Okay, so I probably should have tested FDXMS first before recommending it. At the very least, NP2XMS works on Neko Project II, so you can try that for now, and I'll see whether I can come up with an alternative. (Plus, you get the full YM2608 sound samples on NP2, rather than the partial -26 on Anex.)
EDIT: I should add that I was wrong when I first encountered the issue. The problem here is the expanded memory, which LLS requires at that point for some reason. FDXMS doesn't do EMS, so it doesn't work. However, all the EMS memory manager setups I have found apart from NP2EMS have significant overhead. I'll keep looking and report back.
EDIT 2:
New archive. The performance of the fd+emm and vem486 setups are about the same, but still considerably slower than without an expanded memory manager installed. Ideally you want to make sure this only loads for LLS.