First off, 220k lines of source isn't that big.
You're not going to solve this with a big bang so get that idea out of your head. You're going to solve it gradually, and for a code base of that size it's going to take maybe a year of relatively slow improvement. Everyone on the team has to be on board, and every code review must include "What has been improved?" and "Did anything get worse? If so, that's not okay."
1) Pick your battles. The code you're not changing is code that doesn't need to be looked at. Address your pain points as they come up.
2) When you find a pain point while making a change, MAKE IT TESTABLE. Since you're in here making a usually simple fix, a single nominal test verifying that fix is fine. Testing anything else is a waste of time. Testable code will improve over time.
3) If you can't make code testable because of an intractable dependency graph, welcome to the hell of "Design Dead". The only way out of this scenario is a rewrite of that area.
4) Find your comfort level with regard to time boxing refactoring work. On my engagements, they just happen automatically, without explanation outside the team, nor apology to anyone. When estimating a piece of work, pad it with some extra time for cleanup. Only actually create work items for design dead areas. Your definition of done must include testable, tested and improved code.
5) Duplicate code in itself isn't evil, and inconsistencies are simply inevitable. If you find duplicate code, pick one and deprecate the rest. However, code that is tightly coupled to the deprecated code will need to be refactored and if the coupling traverses an extended dependency graph, you'll simply have to live with the duplication and just stop adding to it.