I was sorry to have to write that, OP. As long as hope triumphs over experience with admissions tutors, the over prediction problem will persist.
The main site for TMUA prep is at UAT UK. I hope they have past papers. These are incredibly important -for practice, for extrapolation, etc, but it is equally important not to get into a mode of memorising ir thinking that the old problems per se are preparing you. Learning new ways of thinking is what’s preparing you. Also, it is important to give the problems an independent go before looking at the model answers. Many, perhaps most, highly able students have never had to struggle and they find it very difficult to do so. Better to learn now than in the midst of a demanding degree programme (or to flail at university because you can’t cope with the very idea - many do).
The AMSP site used to have a lot of support for TMUA. However it may have been migrated to mei.org when HMG reallocated funding a little while back.
Perhaps other MumsNetters can recommend good professional tutors for TMUA. But another option would be to try advertising for a student with good teaching or tutoring references at the London universities or Southampton. Really, it could be a someone with good tutoring skills and very strong personal maths ability at any level; UGs in Maths, Economics, etc from some of the London universities will have recently cleared the TMUA hurdle themselves. MSc students will have more mathematical maturity. Six of one, half dozen of the other. (Funded PhD students will be too busy, and in STEM or Economics I don’t recommend the others for this)
The online forum The Student Room has a good advertising service for tutors. DS could join and might find something there. Or, he could post the need for a tutor as a question targeted to different degree programmes (by name). Obviously he needs to make his family’s involvement with the process very clear.
But he can develop a wonderful professional life from Bristol, if he makes good use of what’s on offer. Very best wishes to him.