Let's assume your current Money installs are a US version that is not Money Plus.
You are not easily going to get Money to not alter file associations. The important associations are for *.mny, *.mbf, *.qif, and *.ofx. One thing you can do is to do a System Restore to a checkpoint that predates the Money Plus Sunset.
Another thing to try if you can is to install into a virtual XP mode if you have that. That would make things independent for testing, except the bit about accessing files on your NAS. I don't know how to work that, but you may.
I think it is possible to install Money Plus Deluxe Sunset while keeping an earlier non-Plus version in place. But yes, the file associations get changed. Reinstalling the earlier version should restore the associations. If you have Money 2005, special concerns
come into play for reinstalls. If your version is 2003 or before, a different concern comes up.
I don't know if this has helped or not. Check back for more discussion.
In any case, I suggest doing the backups to the individual computers. If you are sharing a *.mny between two installs, manually make sure that the same file is not open at the same time on different computers.