So, basically I'm trying to figure out how to hijack this project and set it right, all without stepping on anyone's toes.

"Draining the swamp" problems are fun, especially when there are people still living in the swamp.

If you're starting from zero (tests), I'd suggest starting with strictly functional ones. If it's a web app, reach for WWW::Mechanize and Test::More (or Test::WWW::Mechanize, which I haven't used yet but am told is worth the effort), and figure out how to write functional tests that drive the application through various scenarios. If you're not dealing with a web app, the idea is the same.

Then, when you go on a cleanup binge, start by writing functional tests to cover what you're about to change, then see if you can get under the covers, isolate the code you're working with, and write some unit tests for it. The combination of functional and unit tests will give you some comfort as you restructure and refactor.

If the swamp dwellers don't want you writing unit tests, and won't be led gently in that direction, staying at the functional level is better than nothing.