Well, the PBQ battery itself fits perfectly in the C5: it clicks right into the bottom slot
and underneath the retainer strip at the back. Alas I need to modify the lid as it is too high when fitted. Inside the lid there are some plastic strips I need to cut back so the lid will sit lower on top of the battery.

Alas, the retainer at the back seems to grab the lower rim of the Oldham battery (which is not present on the PBQ) so I had to make a spacer of about 17 mm between the retainer and the bottom. Now it sits firmly. I have modified the lid with a Dremel tool and made two small thick brass strips with a 6mm bolt on which the original nuts fit. From the top it looks quite original.
So far so good, still the keyswitch block does not make a reliable contact, I need to wiggle it a bit to get connection.
More investigation needed.
Next step: check the 'grease status' of the motor, wheels, steering and pedals.