Hmm. Are your graphics drivers up to date? Are you able to run other OpenGL games smoothly?
It really sounds likely that this is some sort of issue with your system. Taking a look at task manager might be worth it, to see if anything is hogging CPU that shouldn't be. Another thing to look at might be your anti-virus software, if it's configured to run aggressively, it
might cause this sort of behavior.
From the "you probably tried it but I should mention it anyway" department, a reboot is worth a shot, too.
Edit: right, partially ninja'ed

It would be very useful if you could confirm that it's actually SS / java hitting the wall 
If that were the case, I wouldn't expect spikes - I'd expect a more or less uniformly low frame rate. Although, depending on what mods the game is running with, it could be spikes - that really depends on how the mod(s) in question are written.
It's also pretty unlikely that it would "hit the wall" in the same way everywhere, since the various game states have very different performance demands. That's why I'm thinking its more likely to be a system issue.