OK RW, I’ll take a shot at this.
First of all, YES, electric motors can be tested. Usually an OHM meter. For an electric trolling motor, I think you’d pull the box/head off the shaft, disconnect power wires, and begin testing. that might be the easy part. If, (and this could be a big if)you have to pull the motor out of the the actual ‘casing’, this is a real big deal as is being sure it’s sealed when done, cause if water gets in there it’s toast! 
I think I’d start by calling my area Minn Kota service center and ask a lot of questions.
My honest opinion is that you have a ‘power draw’ working against you as you run your motor. A SHORT
is what comes to mind. If the motor checks out, then it’s one or both of your batteries. Batteries can charge, but can draw down fast because they too can have a short. I know you said they have 26+ coming from them, but that’s obviously sustained amp/hour draw?
(sorry for my rambling)