I think we're getting the same idea.
The AOE is off on the first tooth to start with, but there's too much gap between the first and next tooth, which alters the AOE of the sector engaging that next tooth, creating extra stress. That tooth fails, the sector gear spins in place (engages that first tooth for the remaining 7-9 teeth of the sector).

Nope he is actually right. By shaving the 4th (3rd after the pic up) I was effectively using the tip of the sector gear tooth to push the piston far enough for the 5th (4th after the pic up) to mesh. In doing so the pic up tooth was cut/notched out allowing the piston to travel forward then the seccond tooth on the sector grabbed the pic up and started to slip again until at some point the piston got pushed far enough back while slipping forward to jam the 5th sector gear tooth into the 5th piston tooth jamming the whole thing up.
I didn't take a pic but you could see how it was jammed when I opened it. The piston was slightly draw back. The sector first tooth was half way up the notch I the pic up tooth and the 5th tooth of the sector was slicing the 5th tooth of the piston off. That is why I posted my question because I could see it wasn't PE but everyone got all up in arms swearing it was PE so I was left ti deduce my own reason. After further looking, and you can easily try this at home with an old piston and sector gear, shaving the first two teeth is fine. The third not so much. The fourth and there just isn't enough pic up tooth depth to draw the piston far enough back for the other teeth to connect simple, stoopid on my part, but that's exactly what happened. Shave 3 1/2 teeth off an old piston and then try to mesh a sector gear with it. Works great until about the 3rd tooth then you can see that it's not structureally sound.

I was just trying to explain exactly why it had nothing to do with pre engagement and was just voicing my vote on why.

A bad AoE can lead to PE which is what the OP avoided by filling down additional teeth. I was just stating that by doing so he created the problem he described.

Can I just say, as an engineering graduate, I have no idea why the idea of angle of engagement has gotten any traction in the airsoft community.

If the rack and pinion are involute profiles, then the line of action of the force transmitted is purely a function of the radius of your sector gear. "Angle of engagement" as a variable that will change pressure distribution or force direction does not exist. By shaving off teeth and having your gears mesh at the 12 oclock position, all you are doing is having your involute profiles smash together at 90 deg instead of sliding/rolling over one another like a proper gear mesh.

Maybe there's another thread on here somewhere related to AoE where I can get some insight on why people do it when the physics/mechanics are so wrong?

TLDR: AOE matters, but it's a short range of engagement, not one specific point.

Weaker nylon pistons tend to get more wear on the pickup tooth when engaged at an angle than when they're engaged flat.
Ultimately though, perfect AOE DOESN'T make any difference on POM and metal rack pickups since they're harder and don't deform nearly as much.
I've had incorrect AOE on my system supercore piston for over 300k rounds and it's got next to no wear on it.
Pretty sure the AOE on every systema M4 ever made is off, clearly hasn't made any difference since those racks last forever when they're MADE right.
Basically it just makes people feel better lol
Although shaving the second tooth does help reduce pre engagement and wear. Sometimes the sector comes around a bit too quick and DOES actually clip the bottom profile of tooth #2 off, which later leads to failure of that tooth. And although that isn't particularly damaging since we shave it anyway, the bit of plastic circling around in the gears IS, and does jam up gear trains.

That being said, the angle of engagement still does need to be within a certain range to reduce wear. As you said, the gear profile is involute, so they're designed to work at a certain range of angles. And I've seen some people be WAY the fuck out.
If the piston is too far forward, the pickup tooth tends to be impacted on the bottom which affects the distance to tooth #3, if you shaved tooth #2.
If the piston is too far back, you can clip tooth #2 if it's still there, or apply all the gear's force at the bottom edge of the pickup tooth which may or may not contribute to breaking off the back end of the piston.

But shaving the 3rd tooth is just plain bonkers. By the time the sector has crossed the gap of TWO missing teeth, the profile is no longer lined up properly with tooth #4, and that causes serious problems very quickly. The teeth are designed to engage tooth to tooth smoothly, with a profile close enough to skip one tooth reliably, but not two.

What I really miss is helical gears. Not for torque transmission or anything (They're kind shitty for torque transmission when paired with radial bearings without being double helical), but just because they were nice and quiet.

Id say you're bang on about the material being what counts. But I'd still maintain the only way to have AOE so far off to matter would be a piston so far forward the first teeth on the sector dont even reach the mesh surface, which can be fixed without cutting any teeth, or a sector gear who's center to rack distance is off, in which case the entire mechbox is improperly designed and no amount of sorbo pad is gonna fix a bad mesh.
If someone can give me a kinematic/mechanical design reason for why I'm full of shit though, I'd be interested to hear it. Til then, there will be no shaving off of teeth in my boxes for any reason I've seen.