For less then the price of a linear supply you could probably build a really substantial LC filter to clean up your existing DC supply. Alternatively, it may be possible to filter out the switching noise from the signal coming from the thermocouple, rather than trying to stop it getting into the signal in the first place.
You're right - it wouldn't be unusual to see more switching noise the more current you draw.
But, there may be something funny going on with your grounding or elsewhere in the system. Are you currently using an optoisolator (as you mention in the title) or is that just an idea? Do you think you could draw up some kind of system level block diagram showing how the system is interconnected?
I don't know, but I doubt that the answer to your problem is anything as drastic as replacing the entire power supply. In fact, it's probably more likely that the noise you're picking up (if that's what is happening) is coming from switching in the motor drivers rather than the power supply.