I don't ever tow with anything lacking a frame, so I may not be the best to ask, but I would first worry about the unibody holding up. They are certainly not designed to tow much of anything, and from what I've heard, there is no stout attachment point for the receiver hitch, and many say the max tow rating on one of those is pushing it.
Automatic transaxle might be a worry (I'm assuming yours is auto). If I had to do it, I would rather have a manual, but it might still give you grief on the ramp, without the additional help from the torque converter. I know that hill starts on our 2000 Civic 5 speed, especially with a few people inside sure aren't easy. Just not enough power at the bottom end. Can't imagine trying it with 1000 pounds of boat behind me. Shocks would be on the bottom of my worry list.
Warranty would be another biggie. I think those things have a pretty good warranty, but I can assure you that if they caught wind of you towing over the rated capacity, much of that will be gone.
I'm not going to say that it can't be done, as I've seen worse tow rating - towed weight ratios at some local ramps, seemingly without a problem, but I can't, in good conscience, recommend it.
No close friends with a small SUV or pickup you could borrow? No need for a beater truck (older used ones can be gotten dirt cheap, and are rather inexpensive to own, provided you carry only liability insurance, and can be downright useful for quite a few things).