An excellent approach to systematically reduce technical debt, well written Bastian!
In addition to the above steps I thought an “inspection” step, which should be done periodically, would help. It is to discover new debt that has been introduced to the systems since the last checkpoint (i.e. 2nd step). In theory the team should not allow bleeding (i.e. new technical debt) to focus on curing the wound (i.e. existing debt), however, it would be naive to rule out the possibility.
Cheers from Singapore 