How to simulate a tire most accurate?

For a project I need to simulate the process of changing tires on a rim.

I don’t know if it is understandable what I exactly mean, so here is a video of the process.
(TC950 Tire Changer Demonstration by - YouTube)

I modelled a rim and a tire in Maya and imported it to UE4.

In the process there is a phase where the guy in the video is using a bar to push up the tire above the rim.
So my thoughts on simulating this process would be to make the tire flexible (e.g. maybe using Nvidia gameworks Flex?).

But that isn’t even the point of my question here. My question is more about the collision that I would have to handle while the user is using such a bar later.

The simple collision for the tire isn’t round at all and I can’t use the complex collision as that would stop me from using physics and gravity on that object.

Am I missing something out? How should I simulate that process for an interactive application?

I was also wondering if I could change the mesh setting “Collision Complexity” during runtime via blueprint? That way I could use the simple collision while the user can grab the tire, but as soon as the tire is on the machine, I would change it to the complex collision.

Maybe it would be easier if you animated it using bones, maybe morph-targets. If you use multiple bones and control their position inside the Editor, depending on the position of the bar, you could “lift” the bones one by one until they are all lifted, then detach the tyre entirely.