in reply to
So I'm in a bit of a quandary
Been there. Bad memories.
Explain that the project will take longer than you thought because you have to trace what is happening to the data at each stage. As you figure it out, fix it and/or document it. You may be responsible for maintaining the code for a few years and might as well make your job easier from the start.
Of course, your boss knows you are only documenting and "applying a uniform format to the code" - not "fixing" what he wrote. "Optimizing" how your modifications interact with the original code comes later. (This will look a lot like a rewrite.)
I spent two frustrating years waiting to start a re-write that was always "two months off". During that time, the nasty code I inhereted just got bigger and more convoluted as we tried to work around the existing problems.