You have two basic choices:
1) Swap grip frames. That can be cheap, or expensive. Cheap is to get ahold of a used Blackhawk aluminum XR3-RED grip frame with factory grips or similar, worth probably $50 and if you're even reasonably good with a wrench, can be homebrew installed. Expensive: there's a "Hunter Model" SBH stainless steel grip frame that is the same size as the SBH grip frame you have now, but with a round guard.
You might find that the smaller Blackhawk/Vaquero sized grip frame fits your hands better than the bigger SBH pattern.
2) Swap grips. Most of the rubber SBH grips fill in the area behind the triggerguard. Blu Magnum (linked at
www.sixgunner.com) has some wood "western lookin'" grips that also fill in the gap behind the triggerguard, eliminating the "Dragoon Bite" you've run into but like the rubber grips, make life rough on those with small hands as the reach to the hammer gets longer.
I'd put XR3-RED type grips on. Aluminum will reduce the gun's overall weight, and are cheap. If that doesn't appeal, Qualitas has XR3-RED pattern grips in stainless or brass, running around $150, or Ruger makes stainless XR3-RED frames for Vaqueros.
You could also switch to a Bisley grip.
More info here:
http://www.thefiringline.com/forums/showthread.php?s=&threadid=80872