The fastest way to adjust your global rating is to play ranked custom 1v1 matches. You get more change in rating for 1v1s because it's easier for the system to recognize that YOU played well. When it's a 4v4, the system doesn't know if you won because you got carried by teammates. So you might only move +-8 points for a win/loss. But with ranked 1v1s you can move +-25 points per match.
You won't find very many custom 1v1 lobbies, so you will have to make your own.
If you really are better than -200, if your "true" rating is 400, you can probably get your rating up to 200 with only about 15-20 ranked matches against 400-rated players. From there you can get into a lot more custom game lobbies and your rating will naturally develop over time.
Also, people's ratings do adjust faster when they are completely new (with let's say less than 50 games) but even if you have 10k ranked games, your rating never stops changing. Someone with 200 games is going to have their rating change with every win/loss about as fast as someone with 10k games. So a reset wouldn't actually do much for you.
I'm going to be blunt here: I'm guessing that your rating of -200 is more or less accurate. Resetting your rating to zero would do nothing for you because you'd just lose a few games and go right back to -200. I welcome you to prove me wrong by playing some ranked 1v1s and crushing it.
And even if I'm right, it doesn't mean all hope is lost. If your -200 rating is accurate, it's NOT hard to improve a little and move up to a rating like 500. You just have to WANT to improve, and work at it. I wrote a guide to 1v1s if you're interested.