No way to solve this, no.
It's one of the reasons why I, and many others, choose not to associate any file types with Media Center.
If you come at it from the other direction, you won't miss out on anything Media Center-wise.
What I mean is this: Instead of organising your files in explorer, then sending them to MC to be played, use MC to automatically import files, find and play files from within MC, and get MC to organise the files on your hard drive the way you want them organised.
The whole system does rely on having your files tagged appropriately within your MC library. Once up to speed with that, it's easy to stay on top of things, tagging new files as they are imported. It's the MC engine room and works really, really well. I cannot remember the last time I browsed my media folders using explorer.
To turn off MC file associations, you can use "Tools > Options > File types" from within MC, but probably the easiest way to go wholesale is to run the installer again and at the file associations page, hit the 'select none' button and continue.
-marko