if you are not happy with a complaint response from the practice manager, you can complain to the CCG using the NHS complaints procedure.
at our surgery, you get allocated to whatever GPs name is down for the allocations on the day they register you, you dont get to chose which GP is "your" gp
If you write to the GP themselves, the PM will just see it anyway, or it'll get opened by the sec and passed to the PM.
you dont need to ask them about their answering protocols - they will be evident when you ring up to ask if they can take you on i guess.
personally, i dont think youll find any surgery is much different, and at least you know with this one how far you are dawn the queue, which imo is better than ring ring ad infinitum or no clue if you are next or 100th