I’m not sure if mint is completely the same, but on Ubuntu you can easily make a bootable USB of another distro using this method: https://ubuntu.com/tutorials/create-a-usb-stick-on-ubuntu#2-requirements
You’d then back up your data, and restart your computer and then, depending on the computer, it might either start the distro installation or you’ll need to go into bios and configure your computer to boot from USB.
It sounds more complicated than it is, but there are lots of online tutorials to show you how to do it. Just make sure to back up your data first just in case.
I had the exact same problem with Ubuntu trying to get steam games to run. Unfortunately I could not resolve it and was advised to move to another distro. I chose Fedora and now everything works perfectly without having to make any adjustments. I know it’s not the answer you’re looking for, but it is a solution.
I had this dread too! I thought it would be incredibly time consuming but it ended up being a 30 min job (when I’d spent at least 4 days trying to make steam work on Ubuntu). Distro hopping is definitely one of the best features of Linux.