Just so it goes into the archives to help the next guy.....
I added coarse screws to the butt joints. Thanks for the tip to clamp the MDF that I was drilling/screwing in order to support it. That would never have occurred to me and I think it helped.
I cut off the solid wood handle and made sure the "stub" was flush. Over the top of that, I glued down another (partial) layer of 1/2" MDF and mortised a plywood handle into that.
I decided it was easier to use the push stick with the handle facing straight forward, rather than canted toward the fence (see original pics above). Since the push stick encloses the Biesemeyer on 3 sides, I decided it didn't need to be angled after all.
Pic of the "version 2" below, straddling the fence with a narrow piece of wood being pushed. You can just see the leading edge of the Shark Guard.
20180107_170315.jpg
Thanks again folks!
Fred