Looking for pictures, description of your strong back support. Mine will need to roll around in the shop as I often jump from one project to another and this canoe is petty big. I have a concrete floor that is not perfectly level and my current plan is to weight, lock cart down to get all my levels and first several strips on then move as needed, problem? What I'm getting at here is after stations are set level, plum and square and locked with first say 15 strips and I move it to a new spot that is no longer level that won't be a problem? Thanks for your time.
For a small project like a kayak/canoe, I don't pay much attention to whether the strongback is level - as long as it's reasonably straight and inflexible, I'm happy. I 'square' the forms to the strongback (automatically) with the brackets that support the forms. (This is using an external strongback, but I think it would be the same with an internal strongback.)
With a wood strongback, I can easily move it (one end at at time) in my shop even with a good size kayak on the forms. I'd never put wheels on my strongback. I use sawhorse brackets to make the 'legs' for my strongback and they are a bit flexible to adjust to the floor. I'd have no problem putting shims under the legs if necessary.
Once you have some strips on the forms (staple some temporary scrap strips at odd angles on the forms when starting) the forms will be 'locked in place' and you can move the project (gently) around the shop.
There are lots of other ways of doing this - mine is only one.