Most recomendations for tongue weight for stable towing are 10-15% of trailers loaded weight, and most folks load their rigs to the GVWR if not beyond. We have a 7500# trailer with 1200# distribution bars and it tows without sway with the combo we have. 1000# bars should work fine for you, but I have no experience with WAY stiffer bars and if it ain't broke, I wouldn't fix it!
2011 Jayco Eagle Lite 256rks 28ft. travel trailer; Reese SC hitch
2010 Chevy Silverado 2500 6L w/3.73 differential
Member: TTN, Escapees, Good Sam
3x around USA, traveling about 6 mo/year