17x11s are going to be hard to get and stay in your budget.
Looking at TT2's they make a 17x11 that is off the shelf with a 7.75" BS, in a 5x4.75, and a 7" bs in a 5x4.50 so yeah you'll be into pretty big adapters, like I think your finding out.
Do you know about what backspace you are going to need? If so, we can built you a 5x4.50 to 5x4.75 billet adapter, so you can run the 7" BS 17x11s and your adapters may not be any longer than 1.5" which is common for billet adapters. Our billet adapters are 75 bucks each by the way, with 1/2 or 12x1.5mm studs.
If you went this route, you could save some money by going with Sumitomo tires, 315/35/17s, which are cheaper than the Nittos.
We have the Sumi's for $138ea. in that size. They also have a matching front, in a 275/40/17 for $117ea.
With a set of TT2's you come in pretty close to your budget.
Let me know if we can help out at all.
