Jacks question

The current will depend on camper weight and lubrication.
I estimate my front jacks carry about 2000 lb each.
When I disconnect the battery, I can use 1 at the time on 40 amp converter, but that gets marginal.
So I would not put wire smaller than 12 ga to each corner and at least #8 to the controller.
Bad part you can't use TC frame for ground, so you need to run double wires.

I have Happijacks, so can't speak to the motors amp draw on yours, but "heavy wires" is confusing. Mine has 12 or 14 gauge wires going to each individual motor- one wire from the mother board to each motor.

Most people wire them permanently and drill holes through the wall, run wire through, seal it and connect to motor.

I decided to just hook up the wire when needed and then put wire back inside camper when not. On the 4 corners I have 4 doors or hatches where I can hide the wires easy. They each have two-pole connectors so is easy. Fridge door, propane door, water/power access door and the fourth wire has to come out of the inside closet and out the back door, but the wires all stay inside this way. It was just easier than drilling holes, which I hate, this way.
It takes 2-3 mins to wire them up.

Its doable. I did this on my TC. You may already have the electrical outlets at the jacks. As said before you need lots of heavy wire plus you didn't say where you are getting the kit. Mine came from a wrecked TC. Some electrical experience will help or a friend that has some. Ron

You will need to run heavy wires to each corner, than find space for control board, where you can run even heavier wires to battery.
Than activation switch wiring.
It will make some project, unless you do interior remodeling anyway.