1960s' convertibles used hydraulic pumps to operate the tops. Perhaps your car went through an inter-dimensional time warp. Otherwise I would suggest either the dealer or a specialist so things don't get worse.
I know that , your.mechanic doesn't. I also know that many times a minor adjustment will fix a lot of 'binding' issues with conv. tops , but that they're best done by someone with experience , that is why I suggest a dealer or specialist.
These tops use electric motors. There are quite a few switches and sensors for the top that if bad, will cause this problem. You really need the proper scan tool to read out the diagnostic codes, monitor the sensors, and reprogram the system, otherwise you are flying blind.
Let me know if you need a place, I may be able to suggest one in your area.