Hi, AVID
I know where you are coming from, I too have RA in my hands, shoulder, knees, back and ankle. This changes your life in many ways and it's not fun. I also have an OT canoe, 14ft 7in Guide. I can't paddle very long without pain and have gone to a trolling motor 2 years ago. The side mount is OK but does not steer well for me. I bought one trailer 2 years ago and if you put any weight in the canoe it would twist the trailer at the ball making the canoe tilt. That trailer was designed to carry only the canoe and you could not carry anything in your canoe or launch from the trailer. It also was painted metal and rusted no matter how much you washed it. I have since bought an aluminum trailer from Castle Craft (on line) a Trailex SUT-200 great trailer, won't rust. You can carry some weight in your canoe without any problems, trolling motor, tackle boxes, ect. (use a pad under theses items) but I do not carry heavy batteries inside the canoe for fear of hull damage from bumps. You can launch your canoe from this trailer with all your gear just don't put the trolling motor on the bracket until the canoe is in the water. To your original question about battery size, I would get the biggest deep cycle battery you can. When I go fishing it is from dawn till dusk (fresh and salt water) and I have been in trouble more than a few times due to wind, current or I just went to far to fast. I now carry two Everstart Maxx from Walmart.
Good luck with what ever you decide to do.
I like Joshkeller's solution.
Keep the open side up :~) Dave