Hi Runner, you could search this forum using a place name near you, e.g. Birmingham perhaps, and check the profile of those who come up to find if that person is having uSPA or a level of psa that you find acceptable. Then find a private hospital that uses their lab.
As said above it could be a worry if found early. Although I went detectable above 0.05 in Dec 21 when I was about to be discharged after 5yrs. If I'd been discharged my next test would be Dec 22 and it still hadn't gone over 0.1 then. So the next test would be Dec 23 and at current trajectory it could then be 0.18 plus or minus by then, which would be a shock.
If you found it was going up you could plan ahead for scans and hope it's a single place, although it depends on your ability to sit tight and not go mad with the tests. I've got more adjusted to my rise and am glad I know.