How I see it: We're playing with effective stacks of ~22bb. Flat calling invites the BB in to a 3-way pot, and we're never just folding, so this question is really about our 3 betting size and if we're calling a 4bet shove.

Can we ever 3bet small and fold to a jam here without any specific player reads?

I'd think Villain's worst raise -> 4bet shove hands are probably JJ+ AJ+ maybe KQs... assuming he just open shoves 77-TT from MP1.

Thoughts?

Call, raise, or fold.

Out of those folding is awful and calling feels very meh to me. Shoving is certainly +EV. Maybe someone who is good enough can make more money by raising but I'd rather take the sure thing unless I know exactly what I'm doing.

just jam readless (odd that every single post you make seems to say you have no reads, while in donkaments you can move tables a bunch, unless it's the first few hands on a new one you shouldn't be readless ever if you're paying attention)

I typically tag players who do things like value bet thin/not at all, capable of folding/not folding etc...

Most of my hands involving strong reads don't require a second opinion. If I believe in my read then I usually feel confident with the play regardless of the result.

What reads specifically do you make note of?

3b/folding would be a bad option. 3b/calling off would be pretty hideous too, as you're likely to be getting it in bad. I'd either call or (more commonly) jam.
A read (or some stats, like VPIP/PFR and fold to 3-bet) on villain would be useful.

I'm confused by this. Are you saying Villain's 4bet jamming range is stronger than his 3bet call off range?

I would think off of that stack size those two ranges would be identical.

Any decent 3bet will be enough that villain either has to shove or fold so you may as well shove or fold. Calling is not a good option OOP.

Generally jam.

Villain should have a raise-fold range. The range that continues vs a 3-bet is stronger than the opening range. Facing a "standard" 3-bet, his 4-bet range might include some "bluffs", it's true, but mostly his 4-bet range is going to be very strong, because he expects you to call off. If you just jam on him, he has to fold many of the hands that he might have been able to profitably 4-bet jam. Making villain fold a lot of hands that could have been profitable for villain is very +EV for you.
It all goes back to one of the (somewhat counter-intuitive) tenets of short-stack poker: It's very profitable to make shoves, and it's not very profitable to call them.
If you get hold of a reshove calculator (like the old pushbot spreadsheet), it can be very eye-opening to see just how profitable it is to jam on openers when you have 12-25bb. They just don't have enough hands that can profitably call, because - by calling a shove - the only way they can win is by making the best hand. If you're the one that goes all in first, you have two ways to win.

Would all the above still be true for a $4 tournament?

Thanks for the explanation. I guess we could 3bet our strongest hands (AA/KK) then to keep Villain's 4bet bluffs in his range.

I've actually been experimenting with reshoves a lot lately, but very unscientifically. Still, they've been profitable for sure. I'll try to find a reshove calculator to fool around on.

Even if the answer to this question is no, I don't want to be playing micro tournaments forever. I'll live even if I level myself a few times.

Yes, you can exploitatively 3-bet small with the hands that want action (QQ+ and maybe AKs), but jam everything else that you want to play. I think AQ/AJs and JJ might play OK as calls in this odd spot though, as they are still ahead of villain's opening range and flop well enough to stack off if you hit. Most of your Ax, suited Broadways and pairs should probably just jam though.