I disagree with this "doubling." It's a rule of thumb with a lot of variance. A better way to think about
it is that Proscar helps get rid of the PSA due to BPH but not due to cancer or other things. So it sets a new baseline for you. The only thing that matters now is what your PSA does from this point onwards. If it goes up, another biopsy may be warranted. I think 3 months is prudent, and I assume you know to avoid sex and bike riding for 48 hours before it.
Actually, I think that PHI would be a better idea. It includes PSA and % free PSA, but it also includes another measure (-2proPSA). It is inexpensive and (unlike many other tests like 4Kscore or genetic tests) it is covered by insurance. I don't know if UCLA is offering it, but you can get a list of local uros who do offer it by calling the number in the link below.
Prostate Health Index (PHI)The other biochemical test that's covered by insurance after a first negative biopsy is PCA3. It's a urine test after prostate massage. The combination of PHI and PCA3 has greater accuracy than either alone.
I agree with your assessment of radiology at UCLA -- Daniel Margolis is the best in my estimation. If you have to have another biopsy, it probably makes sense to have a transperineal template-guided saturation biopsy. It's the gold standard and the only way to make sure they cover every area.