Quote from "The Backyard Orchardist" by Stella Otto

"Most Asian Pears require cross pollination. Either another
Asian pear or a domestic variety is suitable as a pollen
source as long as their bloom periods coincide"

That you know already

However, she does NOT say that Asians will pollinate
domestic pears, but one would think that pollination would
happen both ways. I grow only domestic pears (Lucious,
Clapps Favorite and Cabot) so I don't have any advice
other than to give it a try.