Reverse not engaging... advice needed

[ga_sport4X4]

98 Explorer Sport
Automatic Transmission

Several nights ago, I heard a small noise from under my explorer as I backed it out of a parking space. I didn't seem to make it completely out of the space before I found myself wondering why my rpms were increasing with absolutely no movement of my truck.

It has yet to engage from that moment. Reverse is the only problem. All other gears engage and shift fine. There were no other problems or noticable signs of transmission problems prior to the popping sound.

The mechanic says it is time for a new tranny. His estimate to rebuild the tranny is $1600 and $2500 for
a remanufactured tranny from the Ford Dealership.

Think it's time for a new tranny?
How do the estimates sound?

 

[Opera House]

Reverse is made up from

The low reverse band and the high clutch (4th) that used to third in the older 4 speeds. If the other gears really do work, the pronbem is probably in the valve body and the transmission wouldn't have to come out. The 5R55E has a history of blowing out valve body gaskets. Check oferation in manual low to see if it is really solid. Try going down a hill in low with no foot on the gas. If engine stays at idle and you keep going faster, it is likely a gasket. Replacing VB gaskets isn't that hard. Dealer will do it for about $800.