Okay. I'm gonna say this straight-up: I don't have the skills to do what I'm proposing here. I've tried looking at scripts, but it just made my head approach the cusp of exploding violently.
So here's what I'm thinking: The Dragonborn is dangerous. Scary dangerous. But more importantly, he's a wildcard. He does as he pleases, and he does it for whatever reason he fancies at that moment. For the Thalmor, the Dragonborn would be an obnoxious problem, especially if he forges ahead to try and stop the civil war before both sides have exhausted themselves.
What I propose is this: A modification to the "Hey, Dragonborn, stop yelling in public" script. Instead of only having a courier deliver him a letter, there should be a chance of a Thalmor hit squad, all decked up in Elven armor, to come and try to ruin his day. I even wrote up a little letter that could be left on the corpses to let the player know it wasn't a random elf attack.
Honestly, I just want to fight the Thalmor more. This would allow that, while also making them more actively hostile towards the Dragonborn. So it's a win-win for everyone!