OK it looks like we've identified the cause of these lag spikes.
ULX logging seemed to be the source of the issue as we noticed significant reductions in spawn times once we disabled logging (longer times are obviously before we disabled it):
ULX will log most events (connects, spawns, deaths) so it could be that this was the cause of the issue all along. I'm going to lock this now but please do not hesitate to contact one of us if you continue to notice issues.