On this ETA 2750 there is a strange gear with two horizontal bars running through the center. It appears that this gear is preventing the proper seating of the canon pinion. Can someone tell me the purpose or proper positioning of this gear that sits under the canon pinion?

The canon pinion should be part of the gear, if you have pulled the cannon pinion off and left the gear with two bars behind, you need to remove both and see if you can re seat/repair the cannon pinion between the two bars or if you need to order a new one.. (that is the friction clutch)

Thanks once again Chris,
This makes sense now that you've explained it. When I took the movement apart these two pieces, the (canon and the ring gear) were separate as if they were made that way, and I didn't know enough to recognize it. But couldn't figure out what kept that gear centered!? How would I go about trying to reconnect these two pieces?
At some point if you're all tolerant enough maybe I'll learn enough to contribute to this forum instead of continually needing advice!

Remove both parts, hold upper section in pin vice and work arms over, snap fit, clean/steam first, once back together friction should be felt when rotating, you can adjust/lube to get perfect friction for setting/running.

Thanks Chris, I attempted the repair as you have described here and was actually able to put the two parts back together. I would have never thought this would be possible to do. That's how we learn, with a little help.
However, I think I've "burred" the drive gear so much that the watch does not want to run. I'll attempt to disassemble and try to smooth it down and try again.

I'm going to need to order a new canon pinion with drive gear for this movement, but have yet to find the proper part number. Does anyone have a Bestfit cross reference for an ETA 2750? Or, does anyone have a Bestfit catalog for sale? It appears that there is more than one part that fits this movement. My watch has the center second hand if that makes any difference.