Thanks for the parts diagram Max.
I tried packing some steel strips in the annulus between the clutch housing and the aluminium tube to make it less wobbly but that didn't help.
Obviously although the BBT clone looks incredibly the same as the Honda they are cheap for a reason and the drive system is probably FUBAR. Pity as the motor goes so well.
Getting in to replace that clutch drum bearing looks a royal hassle and may not fix the problem anyway. Will probably just keep using it until it self-destructs.