I think it would be too much moving and if not too much moving, too much failure which prevented the moving, if you know what I mean...either way, bad.....and that's the effect on your DS, not the embarrassment if broaching it with new school, which is actually far less the concern, although seems to be the thing really worrying you.
I can see that if you can get your place at 7+ in a school which guarantees entry into the Senior without exam, that's great and might relieve later stress. People try that (as you have) and either succeed or don't (as you haven't). Most then accept what has happened and focus on the next normal entry point which is 11 or 13. Some will have another go at 8 or 9, but understandably this raises eyebrows in terms of stress created...because again there is no certainty and so yet another application at 11 or 13 may well be necessary.
Your situation is potentially even worse than this, because you are factoring in an additional move to a new Prep. This generates even more potential change - so possibly being in 3 different schools in 3 years - is avoiding 11+ or 13+ really worth putting a child through 3 schools in 3 years?
I think you are trying to hedge your bets too much. There are consequences for your son of doing this. You would be hoping for the 3 schools in 3 years outcome - that is the aim of the exercise....think about how crazy that seems. Your DS would start a new school knowing he was about to sit more exams - how could he ever emotionally commit to that school and make friends and get the best from that year.....and imagine then staying, when that felt second best.
I think that you need to stop trying to hedge. Either choose to remain where he is and have another go at 8+......but to be honest, that's not a great option, because although it could avoid 3 schools in 3 years, if it doesn't work out, you'll still want to move him and be dissatisfied.
I think the best option, if you don't like the current Prep (and be sure you're not just a grass is always greener on the other side kind of person, who will actually always be unhappy with the current school) you should move to another good Prep, but with a view to staying until 11 or 13. Accept that the Junior phase entry to those top Preps hasn't worked out and make the most of the Prep he can be in and do well in and enjoy the rest of the Prep phase. Be confident that he will be well prepared for 11+ or 13+ and do his very best....and that if he gets into the schools you'd prefer, that's fabulous, but if he doesn't, there will be another great alternative for him.
You cannot control absolutely everything. Trying to do this and always seeking after the very best or the very best door to the next phase, is exhausting and not good for a child.
And stop thinking about it in terms of telling the new school - as if that were the biggest barrier. If doing the 8+ really was the best thing, this should be the least of your worries. The thing is that 3 schools in 3 years should be concerning you most. Move school and throw yourselves into that new place for the remaining years. Accept that the move to the junior school of a senior you'd like him to go to, just hasn't worked out. This will allow him to move on from it too, rather than having a sense that really, only there is actually good enough.