DTC P1722 indicates gearbox default to 5th gear. Without reverse you are probably correct on the A drum failure. At any rate probably looking for a trip to a good transmission shop.
DTC P1647 indicates a defect in the upper oxygen sensor on B-Bank. That would be the upstream sensor on the left side of the engine before the catalytic convertor.
P1000 merely indicates all monitors are not set satisfactorily and when change to P1111 when the other DTC's are fixed.

 

 

If it is a speed sensor failure you can read through both input and output shaft sensors ( 2 ) 4 pins at the transmission ECU as they should read the same resistance as a fundamental test as they function as a pulsed wave to count the revs .'

You would have to read them after they warm up as this is a mode of the windings heating up and opening up the wire .

There are also reports of the on transmission itself connector getting contaminated from fluids from above . The connector is a push / pull type of connector like a air hose I believe .

Transmission pressure regulator change to the upgraded one recommended before " A " drum mechanical breakage .

See page 63 keeping in mind the SC engine uses a different MB transmission

http://www.jagrepair.com/images/Auto.../jagxj2001.pdf

 

Been there done that. Reverse only and no forward gears and slight movement at high revs is A drum. The XJ8 has the BMW trans. If you are handy you can do an advance search and find details for swapping out the A drum. If you want to try it yourself let me know I have the workshop manual for the transmission.

 

might take you up on the d/l , forgot to mention i drove it home 300 miles and it was faultless A drum issue or not lol