I agree with the OP, and after reading the other comments I have a few thoughts.
If you do choose an all ad or ap team, get early pen. Adjust builds to include more pen. You know they're going to build more resist, so counter that early.
If you only play one champ, you need to expand your horizons some. Get at least a few champs for each role (or your top two roles) and get decent with them. I personally find it nice to change things up, and having a wider selection helps counter lane opponents and deal with bans. You don't have to be a god with all of them, but at least have a few reserve champs. It'll really help the team out.
For example, when I top, I like to play Garen. But I have Rumble and Gangplank as backups, and I pull them out when Garen isn't going to cut it. I'm not the best gangplank, but I can play in lane well enough and help out with ults.
This doesn't mean that you need to pick someone you're unfamiliar with to help balance out your team. Don't feel like you need a mage and pick LB, even though you've never played her. You aren't going to do well. But take some time to try some of the free week champs and see if any of them are fun to play. Pick them up if they are.
As far as builds go, 9 times out of 10, if you build something straight tank, you can do just about whatever you want and still be helping. Just build HP and resists and muck around in team fights. You won't die quickly, which allows you to be a bit slower on combos/plays with a champ you aren't as good at. If the enemy team focuses you, you're soaking damage for your actual damage dealers. If they don't, you're in their face being disruptive.
Basically, no matter what you choose to do, you will need to react to your team's decisions. You really can't do the same thing in each game and expect great results. Be flexible, work together for the win. There are many options on how to do that.