Tips on Countering High Mobility/Utility Disengage Combs?

Lately I had a lot of struggle against champions that were able to kite me to shut down most of the teamfights and engages we tried extremely effectively by picking champions that were really mobile combined with a lot off cc. Examlpes for Champions like that are Poppy, Gragas, Tristana, Kalista, Lissandra, Lulu, Braum ... I guess you get the idea.

My champion pool on the other hand consists of toplaners and junglers that are all reliant on getting into the heart of the enemy team to be useful. Nocturne, Amumu, Sejuani, Mundo, Singed, Gragas, Mao, Darius etc. The only of these 2 champions I had reliable success with against such combs were Gragas and Maokai. With Gragas getting banned and picked by the enemy team more and more, I can't really rely on only these few anymore, so I need new picks to make my championpool more versatile.

Yet I've gone through a lot of champions that I've mentioned and I feel like that most of them seem to not be able to counter at all. Let's take Lulu for example. She is able to kite pretty much everything that is melee. If you try to passively farm against her, she is able to bully you out of lane instead. I have thought about and tested a few ranged matchups against her and while I think it's a good way to counter her by poke and outranging her, I'm really bad at ranged champions in general, because I don't play them at all. Even at the LCS there seems to be little that can be done to stop them, even though I might not have enough experience to judge on that.

So I thought I might aswell ask you guys. What champions were you successful with when playing against such combs? I think having someone answer me with practical experience will help a lot more than only theorizing it.

And please don't start spamming comments like " Boo Hoo can't counter anyway OP rito pls ". Does not help at all, you might aswell make your own post for that. I'm looking for actual advise here.