Finally!
Oh happy day - it works!
The problem is that the channel in the MP10 charging handle is much deeper than the Channel in the Raptor. All other dimensions (except for that nub at the end) appear to be the same for all practical purposes.
And here's all it took for me to do it....
(Warning: to find anybody less mechanically capable than me you'd have to advertise on the Internet. So if I can do it, I can't imagine who couldn't - BUT, there definitely is the potential to mess up your expensive new non-fitting Raptor charging handle.)
1. - Dremel tool
2. - Dremel bit #100 (it has a round 1/4" diameter head)
3. - Patience
4. - Patience
5. - See number 4 & 5 - repeatedly
First - I removed the nub on top of the charging handle using a small file.
Second - I took the Dremel and "slowly" proceeded to deepen the channel in the charging handle from the front end (end near the barrel) for a length of about 4" or so with the charging handle secured in a vise.
Third - I put the charging handle and bolt back in the upper and checked to see if I was making any progress. Still binding? Back to the vise.
Fourth - I repeated the second and third steps over and over and over and over again. There's where the patience comes in.
I was more concerned about ruining the new charging handle than I was with getting the job done quickly. Likely anybody else could have done it faster, but it works and that was the goal. YMMV.
Now it's what I wanted in the first place.
Rainier should either make one of these specifically for the MP10 (like Tacticool has suggested), or state on their website that it probably won't work without modification.