Well DMB,
Mint is pretty feisty and seems to come up all over the place.The only luck I have had in keeping it contained somewhat is to plant it in dry shade.
You will need to remove it in the spring and just keep plucking any seedlings out or leave that area to the mint and catnip and container garden your other herbs. Please keep us posted.

Here is a link that might be useful: Our pond and gardens

Nah, you're not doomed... as long as you really like mint and catnip.

I've actually gotten rid of mint. It only took two years of pulling, but it went. Prolific seeders are much harder to deal with. I'm not sure I ever will manage to get rid of the lemon balm.