I found the answer to this issue here: https://forum.step-project.com/topic/7471-new-game-carriage-to-helgen-doesnt-move/
Apparently, the creature pack was interfering with SKSE in weird ways. Initially, I still got the "SKSE has quit working" error, but everything was behaving normally. I re-installed SKSE after this, overwriting all the files, and didn't get the error anymore. I can only assume there is a log somewhere in SKSE that was holding a record of the files.
That fixed the start-up issues. Hopefully, this means I can finish re-loading the disappeared mods and continue as normal.
Completely off topic, but I have quite a few armor mods and followers I'm planning on adding later, and would probably push me past the limit. I'm hoping to merge these into a single pack with merge plugins via MO2. I've never used anything like this in the past, so hoping someone can refer me to a detailed reference of how the process works. In the mean time, I'm just happy to be able to play again, and hoping the same issue doesn't happen again.
