OP, not sure where you live bit I see the 135L sell for around $800 a few times per week on the POTN but/sell forum. You can certainly get it way cheaper than $1K if you are willing to buy used or refurbished.
The 200 2.8 L is pretty much the first cousin to the 135L--similar build and size, sharpness, IQ and AF. I use it to shoot field sports with on both my 60D and the T4i I borrow as a 2nd body and it is noticeably better all-around than my 100 f2. I'm not knocking the 100/2 by any means, great affordable low-light/portrait lens. But if I have room to shoot with the 200L, I choose it almost every time. Sometimes there are just times you need to shoot at f2 to get the shot you want.
I think you will be stunned by the quality of most fast primes over your 18-135, although it is certainly a handy all-around lens. USM lenses are just so nice to shoot with, and the IQ of that 135 will be a revelation. My 200L sure was.
Sony A99ii, RX-100ii, Sonnar T* 135mm f1.8 ZA, Planar T* 50mm F1.4 ZA, 24mm f/2 SSM Distagon T*, Minolta HS 200 2.8 APO, Minolta 2xTC APO, HVL-F43M