Do you not have the standeard by-law that forbids people from parking on common property?
Also, about 10 years ago I suggested to my building’s committee that they find little corners of common property, mark them as motorbike spaces and rent them to owners.
The owners corp now not only gets another revenue stream but there is a precedent for not allowing bikes to be parked willy-nilly on CP.
The strata manager is not only nitpicking but wrong. There would be no need to change the strata plan as the common property is not being sold, just leased. I suspect he is only coming up with excuses so that the EC members can do as they please and he can keep his contract.
If you have the standard by-law, you can take action at Fair Trading against the parking thieves. But a better idea would be to identify the spaces and suggest a plan at your next EC meeting (with a veiled threat of what might happen if they don’t consider it properly).