RRP said:

One more thought - couldn't a well placed set screw keep the motor from falling out and on the other end a simple strap of metal screwed to the ring to also keep that end from falling out?

You really want one of these Jotissereies to work for you! 

Sure it would be easy to apply the fixes as you describe. However you then have the fun of loading up the roti and then carefully flipping the whole rig upside down and fitting it on your Egg.

Please promise you'll make a video of this if you do it.

In case you haven't already seen this, here's a video from about a year ago of the Jotisserie that has some closeups of the motor mount and right side spit rod opening so you can continue your brainstorming. 

https://www.youtube.com/watch?v=8dKDQFX4VcU