Here's 4 moves/concepts to improve your game..
- Hand fighting. You can neutralise a lot of wrestling attacks by maintaining good body position, actively controlling your opponent's head, and controlling grips throughout the standing exchange. This will force your opponent to make mistakes.
- Counter-wrestling. Counter-wrestling is using Jiu-Jitsu to counter wrestling attacks. Examples include a guillotine off of a double leg or a kimura trap off of a single leg. Some of the best times to attract submissions are when your opponent is heavily invested in an attack.
- Wrestling without shooting. Just because you can't hit a double leg like Jordan Burroughs doesn't mean you can't take down a resisting opponent. A few good examples of takedowns that don't require a traditional "shot" are snatch singles, snap-downs, and slide-bys.
- Basic Judo. When I first learned what Judo was, it was by watching highlights of crazy throws online. However, the translation of Judo into English is "the gentle way". Instead of thinking about crazy hip throws ("uchi mata" or "harai goshi"), try learning some foot sweeps ("ashi waza"). Make sure to brush up on your Japanese.
Most Jiu-Jitsu guys struggle with wrestling because they try to wrestle exactly like wrestlers. You probably won't be able to do this unless you're young, talented, and very athletic.
Instead, try focusing on building a stand-up game that works for you.