Initially to reproduce the kick/crash I would need to join a public server with mods, such as exile or a wasteland server that allowed certain mods.
Now all I have to do is join any server mods or not, as long as I am not hosting. I think I went into most of the reproducibility detail in the Description section.

This section isn't very detailed because it happens every time I play and is done seemingly for no reason.

What I have tried to do in order to solve the problem:

Verifying game files more times than I can count
1x Game Reinstall
5x Battleye Reinstalls
2x Profile deletions
Uninstalling all mods so they aren't subscribed on the steam workshop and not on my pc, and reinstalling them. (I still got kicked on vanilla servers)

Im sure that an admin will need some kind of log (which I have enabled) or something to figure out what is going on. I'll reply to anyone who comments with what they need, and I'll comment for updates on what happens as well.

Things I suspect are causing the problem:
I have created a lot of scenarios. Like 50 gigabytes of scenarios. It feels like to me that every time I make a scenario, whether I save it or its just me throwing something down quick to test something that the game gets a little bit slower and the kicking problem intensifys a little bit more.

I use Zeus a lot. Same thing, when I use Zeus the game seems to get a little bit slower.

I suspect it has something to do with my profile or something my profile did to affect the rest of the game. I transferred my profile from my old pc to my new one a while back, about a year and a half ago. I played a little bit on my new pc without transferring profiles, and it ran so much faster. I also never got kicked. I think I played 20-30 hours like this. Once I transferred my profile to my new pc, the game became a ton more sluggish both in loading in, and the frames i was getting in game. I suffered a 15% drop. Today I get 30-35% less frames on the same mission or on the same server than I did before I transferred profiles. I don't think this is a coincidence.

I mentioned above that I deleted my profile twice. I did. I moved it to a USB drive, took it out of my computer, and the game still ran more sluggish, although I noticed there was an overall 5-8% increase in frames. I would assume that if it was just the profile, than all my problems would have been fixed there, but they weren't. The 5-8% increase in frames and no kicking (although I only tested on vanilla servers, and this was back when I wouldn't get kicked on vanilla servers) made me continue to believe that the profile or something that the profile did to the rest of the game even after being deleted ended up causing my problems.

The Spread:
At first I never saw any one else got kicked, and no one mentioned to me a drop in performance, but in the last 3 months it seems like this bug has spread. On exile servers, people are getting kicked for SC just as I was. Sometimes there were longer pauses in between kicks, sometimes it seemed to be worse than what I was experiencing. I noticed that it would take them a couple minutes before they fully loaded into the server as well. This makes me suspect they also were having loading/performance issues, but I couldn't be sure. They could just have potato PCs. It never occurred to me to ask them about their specs or what was happening, because I was too busy being frustrated at me getting kicked.

The Ugly: Recently one of my friends in particular who seemed to be avoiding the problem suddenly got kicked for SC more than I did. He never created scenarios or did any zeusing, but he did have quite a few kits saved in the virtual arsenal from private missions I hosted with him. This seemed to piece it all together for me. The getting kicked and performance slowing was all down to the profile. Scenarios, mission save files, kits, other data, etc.

So in conclusion, the issue of getting kicked due to a signature check failing or timing out has extended far past me, and even far past it simply being a SC issue. Its extended to many people who are at various stage of what Im calling "Signature Check Disorder". The getting kicked on the vanilla checks for no stated reason in chat. I even asked a server admin to check his logs to see what it said. All it said was "____ was kicked". No reason.

Please help me and others play Arma again.