I pinpointed the problem to a .dll file from a mod that gets injected through SKSE. The dll in question is “hdtSkyrimMemPatch.dll”, which seems to be a requirement for a mod that adds Bullet physics, and obviously tries to deal with some of the memory issues vanilla Skyrim has.
In any case, if anyone else comes across problems with SKSE it’s highly likely it’s yet another dll file causing the problems.