...so I decided to make a new base plate for the router. Here's the old one. You can see why it slipped off...there's way too much clearance around the router bit.

I found a scrap piece of lexan and transferred the mounting holes from the previous base plate.

Once it was screwed to the base of the router...

I used the router bit itself to drill a hole.

That hole was used as a pivot point to sand a concentric radius along two sides.

...and the sander cleaned up the other two sides.

Then a larger router bit was used to open up the hole in the base plate.

Result: no more tipping router. This new version came out great.

Ready to clamp in the vise for bending...

...like so.