I'm baffled.
You do not go to a CAMO on a one off basis. That would be ludicrous under the scheme as planned.
What would happen is that the new CAMO would have to go through your documentation in great detail, raise the paperwork for the issue of an ARC , suck in their breath and say 'did you realise that your last MO didn't do this, that and the other, so we'll have to do it all over again....' They'd even question your own record keeping, as they have a responsibilty to EASA (as well as having to fund their aprovals)
On the other hand, you could sign up with a CAMO who would do the work, keep the records and for up to 2 years you don't have the effort or cost of a full Star Annual - the CAA and EASA really want this to happen, so have loaded the costs accordingly.
Now if you have shedloads of money or are unhappy with your MOs, then you can 'be a tart' and move between organisations. Otherwise we are being 'encouraged' to stay with an organisation that knows our a/c.
Problems come when our chosen MO decides not to carry on, or when we buy an a/c from another area of the country. That will really hurt