Progress definitely can be made with FIRE with part time work - it all depends on how much money you'd be getting for part time. But as long as your savings rate is still at least 50%, then you're on a track to eventually FIRE.
The thing about maintaining boundaries and not overcommitting yourself sounds like a great thing to work on, so it's worth seeing how that works out and if your life feels more balanced. But yeah, if you are really really struggling with full time and the idea of the minimum 5-10 year timescale for full time work fills you with dread, it's definitely possible to make progress on FIRE with the right part time job. Having had an employment history where you have worked full time puts you in a better position to be paid well for part time, too.
I'm disabled so I've only ever really worked part time except for right when I started work and hadn't realised I couldn't cope with full time yet. It's been much better for me mentally to be able to use the extra time gained from part time work to maintain my life in balance, than to try to cope with full time in order to be paid more. Though I have ended up stuck in work that's a bit low paid, but with a good work history before you go part time that shouldn't be such of a problem. But I've still had a reasonable savings rate every year.
If you're in the USA do remember to also consider whether the part time work provides healthcare.
If you *can* stick out the full time work for 5 or 10 years, you'll be able to go completely work free sooner, but part time is definitely feasible as long as your savings rate is still high enough, and allows you the benefit of getting your life a bit more back under control right now.