you got it right hot pure and simple. by the time you ran it till it wouldnt engage anymore she was quitew warm inside.. and then continuing to drive it backwards heated it up even more, a stiuck valve in the body is a good bet as to what happened.. you likely had quite a bit of clutch material go through that tranny as getting them hot will wear the clutches quite quickly. filling it up with fluid and then vibrating it down the road likely freed the valve and not it operates correctly (for now)..
when you run the fluid low in an automatic the pump sucks a mixture of air and fluid.. the fluid foams up and the line pressure is low. (if this is an AT545 they suffer from low line pressure anyway).. even low on fluid they will run in reverse and not forward as less of the valve body gets filled with fluid (more goes to the pan) so the reversing gear can operate even if the forward gears slip horribly. which when trying to make a trans drive forward and the engine just revs, you have an pply piston putting lackluster pressure on the clutches.. and you have clutches spinning with little to no fluid.. yeah she gets hot quick..
whether tha trans is destroyed or not remains to be seen. removing the pan and finding lots of gray / silver sludge in the bottom would be the true tell-tale sign if it was hurt at all..