That sounds like normal behavior for the GK500 Series. When on the transport wheels, the sprag bearings lock the transport hubs to the axle (in one direction only) and the axle/traction drum is locked to the reel powertrain anytime the traction clutch is engaged. Disengaging the traction clutch lever at the top of the belt cover should get the unit free-wheeling.

 

Thanks very much for your reply - really appreciated! I had expected to be notified of any replies by email and that didn't happen, so I only just saw your reply, so apologies.
Anyway, seems pretty weird to me, but I guess groundsman who mow greens only ever go forwards and then turn around in loads of space either side of the green! In my garden, littered with flower beds, it's sometimes necessary to mow into a corner, then pull back to turn to (say) the right, and get going again. One can sort of spin the mower through 90 degrees as the differential allows one roller to go backwards, though the other is locked.
Once I have it all up and running, I'll probably sell it on via eBay and take the loss! In trying to fix the reverse problem, I disassembled the 'dog' clutch for the reel and removed the belt cover. Both clutches (one for the reel and one for the drive) were missing all their set screws, ball bearings and springs, which I am replacing. However, given my limited understanding of these things, I would have expected the reel drive pulley to freewheel on the reel shaft, so that engaging the dog, in turn keyed to the reel shaft, would transfer the motion from the freewheeling pulley to the reel shaft when engaged. However, the pulleys are locked solid onto the shaft, which doesn't seem right to me - before I start trying to remove them, can you confirm that they are supposed to freewheel on the shaft/

Thanks