Well I don't understand why you want a solo experience in your moba games. I mean aren't team games made to be team oriented? If you want a better solo experience, why not play a single player game?
Because all the other single player games are boring all the time (or more precisely, get boring quickly)? A moba is really fun when my solo skills have a meaningful impact but that's far too sparse for my taste.
Well these are two separate issues you're raising, which is why I'm getting confused:
1. I want to have a good solo experience.
2. I want my individual skills to have an impact.
Your individual skills can have an impact while not necessarily being a good solo experience, and you can have a good solo experience with your individual skills not necessarily having a huge impact.
If you're looking for your personal skills to have a big impact on the game, I think DotA is the way to go, because your personal skills as a player can have a much bigger affect on the game than in League. If you're looking for a better solo experience in a multiplayer game, I'm not sure what to tell you.
The only multiplayer games in which you can kind of ignore your team and still be successful, are games like Counter-Strike where if your personal skill is high enough, you can basically win by yourself; or an RPG like Diablo 2 where if you're farmed enough, you don't really need your teammates to be successful. I have no idea how to make a team-based MOBA game more enjoyable for each individual player (if their team sucks).