I wish to state that your name was not divulged to me but the lady I spoke with at the PET Scan Centre, said, when I mentioned somebody had posted they paid £1,800 pound for the scan, she "knew the person I was referring to" and offered the explanation I posted. This lady, whose name I can't recall, also conferred with a colleague called John and came back with the figure of £2,500 for a private patient with referral fron a consultant elsewhere, Also, she volunteered the information that it was available from them on the NHS only for patients of their hospital (Group) and furthermore the "referral must be from a consultant working at the (their) hospital".
Certainly, as an NHS patient one can be referred to an area of another trust for treatment (although we have in the past had members who wanted to transfer to another trust for a treatment not available at their own but were refused by their own trust. A particular case I recall was where a man wanted Robotic Surgery but this was not available at the time from his own trust but this refusal may have been an isolated case). However, as regards scans, particularly the 68 Gallium PSMA which is not yet generally endorsed for NHS patients, the situation is rather different. My consultant at The Royal Marsden told me he hoped to be able to offer NHS patients this scan later this year but could or would not say when. He was happy to refer me to The Paul Strickland Centre for the scan as a private patient though - it being very significantly less expensive than at the Marsden.
In a quite lengthy conversation I asked whether G&T had their own 'Generator' to produce the tracer and was told no and that they had to buy it in specifically for each patient so it was ready just before the scan. This reinforces what The Paul Strickland Scanner Centre told me was the case in as much as they and all the London Hospitals bought in from the one sole supplier. Clearly the hospitals are over a barrel due to lack of competition and also without back up in the event of break down in supply (as happened to me recently. The situation is likely not to improve until general NHS approval for the scan is given and more hospitals do, it thereby increasing the need for more generation.
I did read through the link you gave concerning the Lu177 treatment. It took quite a time because it is long and written in medical jargon. When actively considering it as a treatment it requires even more intensive evaluation and comparison with alternatives. It even states in part that there was some contradictions. Another aspect about which I had some concern that results were largely focussed on PSA figurers rather than extension of life, although perhaps more time needs to elapse before this translates more accurately in longevity. Some of the side effects were covered and in some cases seemed to be severe but as you say this has to be compared with alternatives and is again an aspect I would want to scrutinise more thoroughly before embarking on.
If you do go ahead you will carry the best wishes of all of us.