OP, I am sorry your family and particularly your DS is going through this. With long expertise as a Russell Group STEM admissions tutor and personal tutor, Mitigating Circumstances panellist, etc, I think this is somewhat complicated.
With four A stars, your DS will find his tribe. Right now you and he must balance what I think is his urgent need to take some time to sort his preferences with the reluctance of many in STEM and Economics to allow a gap year; the worry is that Maths skills will be lost.
I have argued, sometimes successfully, against the latter for very high achieving pupils (our offer is higher than AAA) and my view is that the priority should be figuring out what your DS really wants. ‘He now says Engineering or Physics’ (rough paraphrase). Both wonderful fields, but very different. And within the former you mostly have to specialise. What would he choose? To me it still sounds like he isn’t ver clear within himself.
From the interests you’ve listed, I am not quite sure why he isn’t considering Economics, or a Joint Hons programme involving Econ and Maths. An excellent programme in this area is a fine way into the career goals you’ve mentioned.
I did just wonder if maybe your DS was rejected at the pooling stage because a lack of deep intellectual commitment or, much as I loathe the word, passion, was coming through. If his real interests are in the economic area, this makes sense. With four A stars in hand and, as far as we know, AL grading next year back to normal, he should be a good candidate for those of the top Econ Schools that allow gap years, which he would need to research - always mentioning his record.
Of course if he learns more about himself and discovers that his passion is Mech Eng or Physics, that is equally wonderful. The big danger of applying before you know what you want - and every experienced academic has seen countless examples - is that it is more often than not a real struggle to engage, both academically and socially. You don’t achieve what you are capable of. Establishing the very competitive career your DS wants is then difficult to impossible.
The idea that your H would kick a child in crisis out of the family home fills me with a revulsion too deep for words. Having said that, the only way the gap year plan will work is if your DS presents and activates a plan showing he is making good use of the year, including keeping up his Maths. Best wishes to you all.