I would agree when we have one come in with no reverse we start by pulling the pan you will most likely find big pieces in the pan (NOT GOOD)

reverse mean hard parts failure it take comb of clutchs working togeather to make reverse.

I think its time for trip to trans shop or time to order a rebuild and install yourself, if it is a hard parts failure make sure you clean the lines out, I normally replace the coolers as there cheaper than the transmission to replace

good luck keep us posted