Assuming your placement of the decimal point is correct and his PSA is ..3, up from .01, then it's time to throw the BS penalty flag on his doctor. After surgery, BCR is commonly defined as two consecutive increases in PSA, generally 90 days apart. Of course, with the introduction of the USPSA, there is uncertainty since the conventional PSA used for so long had undetectable at <.1 so then anything .1 to .019 was reported at .2 and thus "detectable."
So, a .3 is considered "detectable," especially if his previous reading was .01. You don't say the timeline for his PSA testing but I'm assuming in the first year after his surgery it was every three months then in the 2nd year every six months.
As to the doctor saying " we'd have to wait six months…" again, BS, it's your call, he can recommend and explain why he wants to wait six months but it is your decision, he simply has to write the lab order.
So, a rise from .01 to .3 may indicate BCR. You are within your rights to ask for a PSA sooner, (it's called shared decision making between you and your medical team) could be 30 days, could be 90 days. If the next test shows a rise to .4 or higher, you've confirmed BCR. If it goes back down or stays the same, ok. I have had mine go from .07 to .16 to .29 (I test every 90 days) then back down and stay there.
If the next PSA shows a continued rise, consider imaging. There are three approved by the FDA, C11 Choline, Aximun and PMSA Gallium (the latter at only two location in California, though FDA approval is expected soon for other locations currently in clinical trial status). The challenge will be at PSA <.5 even the most sensitive imagining will locate the site of the recurrence 30% of the time. It jumps to 60% when PSA climbs to .5 to .99 and 80% at 1.0 to 3.9. A 2mm tumor has 8 million cells, a 3 mm tumor 27 million cells, PMSA can detect those, a one millimeter tumor has one million cells, PMSA generally cannot detect that.
If you decide on treatment based on the clinical data – his pathology report, PSADT and PSAV, time to recurrence, then consider that more and more data sows the recurrence is not limited to the prostate bed but often includes the pelvic lymph nodes. So, imaging may inform your treatment decision. Consider systemic therapy which would combine some form of ADT for a limited duration, six, 12 or 18 months with radiation to the prostate bed and pelvic lymph node fields.