I don't know enough to say whether the controls are a problem, but having just had to replace mine, I know a little bit about taking controls apart.
Your controls don't sound familiar, though. The two types I've had are from the 70s and 80s, and both have to unmounted from the side of the boat before you can take them apart, as the screws are on the back. But be careful, sometimes pieces will come springing out at you when you open the box up.
If you do get it open, what's inside won't make any sense initially, so might not be helpful. Better to try checking the motor, first.
Actually, for SURE check the motor first: if you really think it's the controller, then you can disconnect the cables from the motor and push on the throttle lever yourself to see if you can replicate the problem. If you can, it's a problem with the motor. If not, well... could still be either.

The joys of debugging...
rodney (only slightly less dumb novice)