I don't think Dr. Mundo needs a "big" rework - My idea

I really don't. In terms of functionality, I think his "theme" is perfectly fine, but the specifics of his mechanics could stand to change a little, as well as putting some more interesting power allocated onto his W which feels like a shitty filler spell ATM. Obviously, his passive should probably be something completely new, but I have no idea what to replace it with.

I'm more interested in these 2 changes for his R and W. I'll start with the R.

-> Instead of making it a massive heal-over-time, change it into a modest duration where all damage dealt to Mundo heals him instead. A shorter duration but much stronger effect would greatly raise Mundo's decision making beyond pressing R as soon as the fight starts heating up, as well as making him much less snowball-dependent since his healing is now based on his reaction/prediction skills rather than simply having lots of numbers. It also offers clear counterplay of simply not hurling your massive nukes at the Mundo when you suspect he'll pop his ult, but overall helps to solidify his job as a potent anti-mage Juggernaut who can soak up everything your AP throws at him and then hit you back just as hard.

-> Change his W into a temporary active spell instead of a toggle. Now has a moderate cast time that, after finishing, cleanses all CC and debuffs applied to Mundo before the cast completed and causes him to do heavy damage over time in an area around him for a few seconds, as well as gaining movement speed. W is currently a shit spell that doesn't really do much other than BM with the burn damage when you're fed. Now, being a delayed cleanse makes it sort of pseudo-tenacity, like Garen's W but with a more predictive than reactive component. Note that R's movement speed is transferred here, giving him better chasing power independent of his ultimate if he chooses to use his W that way.

I think his Q and E are quite fine the way they are. Mundo should IMO still be a mostly/full-tank build champion.