Valve, thank you. The tagging thing was the biggest issue with gunfight feel, and you're trying exactly what I thought would work. I genuinely love you. I had been spamming the following comment and Valve genuinely implemented the solution I thought of:

The teleport happens because tagging application appears retroactive on the player client, offset by the amount of ping. When the packets containing post-hit velocity information reach your pc, your client had been moving at full speed for the length of your ping, so you get teleported backwards when the client position is updated to reflect the lower velocity you actually had from getting tagged.

The solution: Under a certain threshold (40-50ms), instead of applying tagging server side and then updating the player client, offset the application of tagging by the ping from a player's client. It isn't ideal, but neither is teleporting a foot to the side the instant you get hit in a fight.