I have just finished getting a replacement transmission in this morning. Same problem - no reverse however all forwards were good.
I looked at just getting the reverse piston repaired however after removing my transmission oil pan I saw that there was a fair amount of ground up fine material in the pan and filter.
Didn't screw around. Changed out the transmission - took 4 hours. Found a great condition alternative transmission with 75K miles on it.

Here is a foto of the filter. You can see the residue on it. If your filter looks like this - don't hesitate - get another transmission or a rebuild.

My experience & forum observations have been that the 722.3 - 5 (nonelectronic) trans. are not very reliable, and are prone for failure once the reverse gear starts acting up. Replacing w/ a used trans. will just invariably end up w/ a failed trans. Rebuilding seems to be the only way to avoid buying a used headache, and getting peace of mind. Finding a good/competent trans. mechanic is the trick. Just my thoughts . . .

You could have fooled me, I was thinking they're about the longing lasting automatic transmission ever made, 2 or 3 times the life of their successors. With even minimal maintenance and respect they commonly go 200 to 300k miles.