Your very thorough cost / wear analysis shows you have a deep passion for this topic.

According to ikea, the main part of the mat is composed of:

“100 % polypropylene, 100 % Polyurethane, Paper, Epoxy powder coating, Steel”

Getting through that steel while simultaneously not mutilating those other layers is the challenge here. If you have to cut through it, regular bits / hole saw are not likely going to be up to the task. Rather than compromise the integrity of the mat, I’d be looking at an alternative cable management system as a simpler solution.

Not saying it’s not possible, but if you’re going through steel, that will be a real challenge.

Google “rafter span table” or “rafter size chart” to get info on what dimension lumber you should be using for various parts of the project. It also depends on where you are located. If this structure will be expected to handle a snow load for example then it’s critical you build it to handle that. What do your local codes have to say about standards for similar structures in that regard?

You realize that if you attempt to pull it out with the car, as it is only as secure as the mounting points…the whole unit may very well give way?