Chain slips off chainrings with a lot of pedal force
I've done something similar - mixing a shimano 105 9 speed triple chainset with a 10 speed chain and a 10 speed cassette and 10 speed derailleur.  It all worked adequately.  It ran fine after a lot of tweaking.
However my chainrings were worn and I had similar slips while climbing.  So I scored some new-old-stock chainrings for the big and middle rings, and all my slipping problems went away.
They happened to be biopace, but that's not relevant.