I believe your reasons for this are quite commendable. While it might be challenging to implement, it's not a bad idea at all.
A simpler way, perhaps, to deal with this is to simply increase the weight downvotes are given in the HNQ formula. At the moment, the formula merely looks at the total score. This is problematic because of the huge influx of 101 rep users and the asymmetric voting that leads to. It has been put quite excellently:
The asymmetry of hot list effect also comes into play here. Those
coming from Hot Questions may recognize the question is crap, and
perhaps 50% of them would downvote it under normal circumstances. But
having only 101 rep, they can't. The 5% who want to upvote (for
reasons that are difficult to fathom) can and do. Result: vote count
that does not represent the opinion of either the particular
community, nor the network at large.
It would be good to counteract this asymmetry. If not at the root, (which is the votes themselves) then at least at the undesirable results, one of them being the way it causes a snowball effect in the hotness points.
One such counteracting measure could be that downvotes on the question (not on answers) could be given a lot of weight in reducing the hotness points. So downvotes would take away considerably more hotness than upvotes add.
This would actually be allowing users to remove hotness points more effectively. But, of course, a much larger group of users.
(Anyone with > 124 reputation.)
Mostly, the questions we would want to take off the HNQ list are the same questions that are worthy of downvotes. (Lack of research, extremely trivial, etc.)
Right now, very trivial questions often hit the HNQ. The questions themselves may "only" get like +25, but the answers often get +60 or more. This is a lot on many of the smaller sites. Due to the triviality of the matter, most of the HNQ visitors can easily recognize that the answers are correct, and thus upvote with a clean conscience. It's not those users' fault, it's fine to vote that way. But the highly upvoted answers do nevertheless contribute to the snowball effect on the hotness of that trivial/poorly researched question. Normally, such trivial content would perhaps not be upvoted so highly nor earn users so much reputation.
Figuring out how much weight to give downvotes could be done by trial and error. Start with one value. If it's not effective enough, then increase it, etc. This way, the sweet spot could be found. Personally, I imagine that quite a heavy weight could be implemented.
This might cause silly, trivial questions to be less likely to stay in the HNQ for a long time. And it would counteract the present effect in which their hotness is a self-fulfilling prophecy.
Would this ruin the HNQ? I don't think so. Rather, I imagine that it would save the HNQ. This way we could have questions featuring more quality and good content advertised network-wide, rather than a lot of the trivial, clickbaity questions we currently often see on the list.
Related: Prevent questions on Hot List from being upvoted by casual visitors (only rep is from association bonus)