Thanks again to everyone for their opinions, experience and advice.
Actual experience trumps theory, at least IMHO. Contrary to my original plan I will not install a tranny crossmember.
Real world testimony by Hotrod Lincoln, Lonnie Gallaher and John1, in applications nearly identical to the one in question, leads me to the conclusion that it is likely that the tranny will be ok-as-is.
Again thanks to everyone for your input.
John