Are there any other champions like Illaoi and Teemo?

By that I mean they are supportive of a gameplay style of pushing top relentlessly, causing the enemy to choose between wasting disproportional resources trying to stop you or allowing you to keep taking objectives.

Illaoi does it because she can 1vs2, sometimes 1vs3 under the right conditions. You'll force one enemy to stay top just slowing you down, and it will take something more coordinated than the jungler + top to stop you if you're ahead. This opens up possibilities for your team to take other towers or win teamfights.

Teemo does it because his mushrooms keep the enemy from ganking you, giving you time to run away then come back and do it all over again. Again it's about opening up opportunities for your team. You're potentially wasting lots of enemy time and manpower if you're not able to take objectives.

I really wish Heimer was functional in this role. I love the idea of hunkering down behind the turrets and daring the enemy team to come get me. Unfortunately, it doesn't seem to work very well in practice because as mid game comes along his turrets have many problems. So he is forced to transition to a teamfight ability caster rather than pusher. However, if you know of a way to make Heimer work in this role, I'd love to try.

There are two champions I've never really played much that I wonder if they would be suited to this playstyle: Darius and Yorick. Darius seems to 1vs2 well, but it's not at all a positional kind of advantage like Illaoi has. It's just being a juggernaut.

Yorick can be somewhat positional with graves nearby, but I don't know how well this style works out for him.

Trynd is the traditional one to do this role, but I don't like his playstyle. He's not about positional advantages like Illaoi and Teemo. It's really just about more being able to 1vs1 anyone, and potentially 2vs1 if fed. But his playstyle isn't very safe, which is not what I'm looking for.