How can I handle a possible poisoned chalice promotion?

a way I can refuse it

First, I would not make a decision until the full package is on the table including compensation and potential growth path. If it's not to your liking you can always say "no thanks". It's probably not going to help your career but it might not harm all that much either.

I'm going to be placed in a position that will absolutely antagonize the people I'll be managing

That is a red flag. Why would an employer intentionally create that type of structure? It's unlikely to be long term sustainable for either party. You can have a discussion with management of what exactly their goal is, what the antagonization is supposed to achieve and maybe make an alternative proposal that is more fun for you and more likely to achieve the company goal in the long run.

still press for the promotion I actually want,

The best way to get a promotion is doing career planning with your boss. Set out the goal, discuss measurable requirements, identify the skill gap, create a plan to close the gaps and than track progress regularly. If your boss doesn't want to engage, they don't want you to promote you.

but I'm probably only adequate at my job.

This may be the core problem here. The most concerning word here is "Probably". The first step is to honestly assess your own performance, figure out where there is room for improvement and than start working on that.

Having reviewed your further comments and your profile, it's probably fair to say the question is unnecessarily oblique about certain things, and misleading about other things.

Now, they say people get promoted to the level at which they cease to be competent.

By your own account, you are already at that level, being "only adequate" at your existing job. And your employer has twice already taken the view that your skills are not sufficiently strong for the next technical grade up.

You say anyway you would prefer the next technical grade up. Is that being realistic at this stage? It's not like you and your employer have a difference of opinion about your technical competencies.

You also say that your past management experience seems to have counted for nothing. On the contrary, you've now been offered an outright management position - a position that may have been created especially for you.

You also say in the question that you will be in an "antagonistic" position in relation to your subordinates - which sounds like a very good reason to refuse the offer - but have since clarified that it will merely involve making tough decisions (or having tough conversations) about other people's competencies when allocating the available work. Which sounds much more like bread-and-butter management.

I think you'd have to show powerful reasons to turn this offer down, given the noise you say you've been making about wanting progression, otherwise you're going to be seen as a Goldilocks or a Walter Mitty.

You may be right to be cynical about management motives, but their end of the bargain could consist merely of getting you a little on the cheap, or filling an unconventional firm-specific role. It doesn't have to be a "poisoned chalice" in which arrangements are made on a grand scale to cause your downfall.

Given that I've been lobbying hard to get a promotion, I don't see how I can say no to this...

You absolutely can.

You have the right to change your mind.

You have the right to change your mind considering the new information.

Nobody is perfect. It's perfectly ok to amend your original request.

I don't have much time to elaborate on my answer, but it sounds like you need to read a book like "When I Say No, I Feel Guilty" by Manuel J. Smith.