So today I told my boss that I'm planning to leave, and gave it a deadline of "by end of year". Though I did tell them that I may leave sooner if I find a job.
The conversation actually went pretty well, and it was a huge weight off my shoulders to start the hand-off process.
To their credit, the work may be terrible, but I think they're doing a good job with my request to leave the company. They even seem to be leaving the door open in case I change my mind and want to stay.
So, I still don't like the work, I'll still be looking for other jobs, but it's been kind of nice to know that it won't be a "burning bridges" situation on the way out.