Word for word, I thought your submission was something I wrote. I've been there, done that, so it is possible. The mess I inherited took me 6 MONTHS to fully comprehend and formulate all plans of attack. Meanwhile, I was trying to fix and maintain what I could.
To tackle the whole problem, where did I start? Everywhere, frankly. There was no one starting point. Everything was affecting everything else. I did my best to get written down exactly what was running on each server, including running daemons, system crontab, and all user crontabs. Basically, build a list of what exactly you can determine. Then, try to get into the mindset of your predecessor and try to understand why (as best you can) to see if that sheds some light on what else may be lurking out there.
I didn't get bogged down in formal documentation because I knew I would have to rebuild everything. I took copious notes and drew pictures of what I thought were the processes of the system, but this documentation was just for my own benefit. Once I could identify unneeded processes, I shut them down or side-stepped them and hoped I didn't break anything; if I did, that was just more information at my disposal. Other processes I simplified and consolidated where I could. Eventually, the system got more and more comprehensible.
Once I "got" everything that was going on, I built a fresh new setup that focused on simplicity and efficiency. This is when I focused on documentation. I kept the legacy system dormant but available, just in case.
Now, we have a darn good system in place. I used virtualization to segregate different services and to enhance security. Maintenance is now preventative. Management is happy because they can now grow the business without everything imploding. The focus of my work today is building new products and services. I hope my successor doesn't complain.