Stopping the Copaxone even for a while as a rule out for your pain would allow you to see if it is what is causing the pain however I'd definitely run it by your physician first. He/She knows your case and should have valuable insight to offer.

I can't speak specifically for the interferons but I would imagine as with other medications you would be more likely to have similar side effects however that isn't guaranteed. For example if one SSRI isn't well tolerated I might still try someone on another depending on the severity of the reaction.

You also make a good point about being able to deal with, and possibly pre-medicating, the flu-like side effects once a week if that is the case with another medication. Good luck!