Sounds like a fine "build".
I can't answer about the Trigger Tech specifically, but my Rifle Basix has plenty of room in an AICS. That said, I had no idea a Timney or Jewel wouldn't fit.
Rifle Basix (which I use) has the exact same dimensions as the stock trigger, so it's not a good judge.
Is it the 2014 chassis, or the new 2015 chassis? The 2015's have more clearance, but they were both generous from my knowledge (I've got a 2015 AX AICS, and it has TONS of room for the trigger area)
It's the now discontinued thumbhole version. Not sure the exact vintage.