Lain you are correct when you say there are other routes to get your Residents Permit and maybe I should have said "reasonable" and not "only" in your case,sorry.
"Choices for temp residence application on the form are (Visiting Relatives, Study, Correspondent, Taking Up Post, Family Member, Employment, Seeking Refuge With Family, Purchase Housing, Maintaining Parents, Fosterage, Other)" are you doing any of the above? I still don't understand why you are so hooked into getting a Residence Permit when you have a 12 month multiple entry F visa?
Vince the best way to find out where you would register if your not staying in a hotel is to ask the PSB, they can give you the address of the police station you have register at and there will be someone there who can speak English