FBW is correct.
I had not checked the figures before posting. If the aircraft (but it didn't) have the book authorised prop, they could indeed have had 20 litres of fuel and been within limits.
So.... If the Pilot believed the figures on the paperwork to be correct, and if he had indeed only 20 Litres of fuel on board, they would have been within the W&B range for take off from Bute.
That would suggest that the LAA Inspector who signed it off (with the wrong prop and autopilot) may have to answer some questions, if that's what happened.
However, the question of W&B departing Strathaven is not so easy to explain.