Hi Ferdie,
If it was me I'd hang my hat on thinking it was a false reading. As you say, a doubling rate of every 6 weeks is very unusual. I wonder how the nurse decided it was definitely correct. Also the surgeon is seeing you next week and didn't want a re-check before then. If I was him or was it her I'd want it double checking before referring to Oncology unless there are other reasons.
If it is correct or anything like it, you should get a psma scan then perhaps hormones and radiotherapy. It will be interesting to hear what the surgeon has to say.
At this time I always have questions in the back of my mind as to whether treatment offered is the best for the patient or what they're constrained to because of staff shortages or whatever. If I suspected it was a delay I'd be looking for ways round it or alternatives. One treatment that shouldn't be delayed is hormone treatment as it only needs a jab, although if you're have a scan you need the scan first. I hope it works out. All the best, Peter