I'm in a similar situation to yours, and I've kind of settled on a similar approach: put out the most pressing fires and reassess 3-6 months down the line. At first I had thoughts to refactor but now I just don't want to deal with the complexity, not to mention I have end-users pressing me. I'll have to tolerate the spaghetti, but at least make it produce correct output.
Best of luck with the migration to DO :)