Having not had RARP either private or NHS, I can't give any direct answers. Having been on this forum a few years I have seen similar questions and their answers. RARP private will cost somewhere around £20k. Some people on here have reported that the NHS doesn't really want to know about supporting incontinence, ED, etc. afterwards, but others have said the NHS has been fine. It probably depends on your local NHS trust, I don't know if you can find out from them in advance how supportive they will be.
If you have been offered AS there is no hurry, obviously you think there is, and that's why you ditched AS. The only known side effect of AS is anxiety, so I guess you could say you're treating the anxiety by having a RARP. Well you are better at knowing which aspects of your health to prioritise than I am.
There are plenty of men on here who have ditched AS, due to anxiety and some because the test results are clearly going the wrong way. There are some who didn't even try AS for two weeks despite it being in the opinion of the doctors the best option. So at least you have gave AS a go and know it is not for you.
By my reckoning October is 12 weeks away, if the doctors consider you suitable for AS there is no way that they think it will progress within three months. A biopsy would not tell you anything useful, it would tell you, you have G 3+4=7 cancer with about 10% G4 but you already know that, it would tell you nothing about whether the cancer has progressed because it is a sample of a small area of the prostate. An MRI would be more useful than a biopsy, but the best test for cancer progression is a PSA test, and from what you have said it is not getting any worse.
If you were really really worried about progression, you may be able to get Hormone Therapy prescribed for three months.
As your cancer seems very low risk you would probably be eligible for the latest radiotherapy, which is about 5 visits to the the hospital over two weeks to eliminate the cancer, and have hardly any risk of incontinence.
As I'm sure you can tell, in my opinion, as some one with no medical training and no knowledge of your cancer other than what you have posted here, I think any money you spend on this would be wasted, and better spent on fine port and Cuban cigars (and I don't even smoke).