According to preflop solves, this is a pretty high EV squeeze spot.

Flop: We are first to act and have slightly less than 1 PSB left, so if this was vs. 1 or 2 regs I would just shove flop without thinking, but we are 4 way with 2 fish who probably have a real vpip of 70+. For them a 422 flop is more like a 988 flop for regs/lower vpip types where they could easily have trips or a wrap.

Do we still shove here? At which SPR and number of players would you start checking?

So using some PPT math - top 15% is 345,000 hands, top 15% with 2x or 44 is about 25k hands, so the odds of one player having one of these is like 7% roughly - not a math guy so maybe I'm wrong here but think this is right. Have to jam here given stack sizes - we still have the gutshot and two queens if we need to improve, but the majority of the time we're going to be ahead here. The other caveat is I would assume they reraise AA - I think most KK just calls.

I agree that shoving seems to be correct even vs 3 players.
I checked some numbers in PPT using the questions feature: How often at least 1 player flops trips+
I'm not sure about the inputs but I tried the following to get some rough estimations:

If we input our hand and 3 players with 15% hand ranges (top 25% excluding the top 10%) we get 23.4%
If we input our hand and 5 players with 15% hand ranges (top 25% excluding the top 10%) we get 40%

Vs. Whale ranges:

Our hand and 3 players with 10%-70% ranges: 46.3%
Our hand and 5 players with 10%-70% ranges: 73.9%

Since we need ~33% equity to get it in at SPR 1, it looks like we can just shove our hand vs reasonable players even 6 way.
Even vs whales we can shove 4 way but need to fold 6way.
Of course this analysis is far from perfect since we sometimes lose to KK, sometimes value bet fish calling with worse and also have 10-15% equity vs trips but I need to start somewhere.
Am I missing something?

Shove is fine as played - Hero could try to construct a smaller size to bet/fold in some multiway action scenarios, but it seems like a lot of work for what i expect is a small theoretical gain at best.

Pre-flop squeeze looked ok, though given hero hand strength and playability, flat is certainly fine.