This villain sits OTB in a 6-max game with a 4bet/call range of TT+ and AK+, and a 4bet/fold range of A5s-A2s. In other words, all his 4bet/folds contain an ace.

We are sitting in SB and playing a "3bet or fold"-strategy and have now been 4bet by BTN and are thinking about what hands to 5bet (shove) with.

We know that he uses AXs exclusively as 4bet bluffs,
so that means that when we shove with a hand like Axs he is more likely
to actually have TT-KK.

So would it be better to use hands like KQs, KJs, QJs, QTs, and
JTs to 3bet/shove?

AJs, ATs and A5s got ~30-32% vs TT+/AK.
22-99 got ~29-31%.
Suited broadways got 29-32%.
... So it's pretty much the same equity when called.

KQs and KJs still blocks AK and KK, and the rest of the suited broadways
block two pairs of QQ-TT, making it more likely villain was 4betting with one of his A5s-A2s that he will fold to my shove.

I have not done any detailed math yet, but what do you think?
Could suited broadways be better hands to shove with than AXs and mid-pockets?

Suited broadways seem to clearly be the best bluffs. However he doesn't really have enough 4-bet/folds for you to 5-bet any of these hands profitably for normal sizings, I think. He's stacking off about 70% even when you hold KQ, which has the best card removal. You should probably only shove something like AK/JJ+, although it depends on sizing.

If you pick sizings it is pretty easy to come up with the EV of shoving each hand.

You are right, I made his 4bet/fold range to small.
Fold equity needed (if I calculated correctly) is about 50% if I 3bet to 9 and he 4bets to 21 and I have 30% equity when called.

Does this mean that he can have a 4bet range consisting of 50% bluffs and be balanced vs my strategy?
That would be a 4bet/fold range consisting of something like A9s-A2s + K9s-K7s.