Griff sorry to hear you are having ttc problems. I am not an expert, but I can tell you what it was like for DH and me.
We had IVF on the NHS so I don't know how this compares to going private but our timings were like this:
End of April: first appt with dr
June: tests for me - FSH, LH, AMH, rubella immunity, HIV status; SA and HIV test for DH
HFEA forms filled in and analysed
July: second appt with dr to discuss results and plan treatment
August: 13th, started course
Sept: 3rd, bfp; 9th, the day I was meant to POAS!
If you go private, I think you won't have to wait as long for tests to be done and analysed. We did lose a few weeks waiting for me to be on the right day of my cycle for tests etc and then, obviously, to start the course.
You can start the course at the beginning if the cycle after all your tests come back.
I have to say, it wasn't the easiest thing I've ever done and you need to brace yourself to pack up your dignity and put it in storage for a few weeks (you need fanjo scans throughout the course to monitor how the drugs are doing). The injections were actually fine, and the hormonal bonkersness I was expecting didn't happen much
If anything, it was harder for DH because I was doing all the "work"
I definitely recommend seeing if a short protocol will suit you as it skips the bit which I think can be really hard, the down regulation.
PM me if I can tell you anything else
Good luck!