Good that she is performing fine in other modes
The problem seems in engaging & dis engaging in reverse did you tried , moving leaver in all positions while pressing brakes
Do it just after starting & also after 5 minutes of starting
before starting the experiment ,
Make sure ride is on flat surface
Put her in neutral & engage hand brake
Now start moving lever in all positions & observed , especially in "R"
move around PRND & also observed RPM drop/raise