Several things to look at here. First... you are going to be a lot heavier than 7300 lbs loaded. On average people tend to add 1000-1500 lbs to a trailer. that means you are looking at 8200-8700 lbs loaded tt weight. What are your trucks rating (payload and tow capacity?)
True sway is defined as increasing oscillations from side to side. Is that what you have? If yes then you need to shift the weight in the trailer as sway is usually caused by improper loading/too light on tongue and heavy in the rear. Move the weight forward of the axles.
If you feel like you are driving on glass and the truck is floating on the road, you are front end light and need to adjust your wdh. If you are porpoising (up and down bow like wave) then you need to adjust the wdh. LT tires (read stiffer tires) will help as well. You will always have a little tail wiggle but shouldn't have true sway.
Now you need to look at your setup. Best thing to do is to go weigh your setup. Go to a local cat scale
or if that is too far try a local feed store or dump station. Weigh fully loaded for camping with all people, gear, pets and full tank of fuel. You want 3 separate weights (can be done in any order). First weigh is truck only no trailer. Weigh front axle on scale pad 1, rear axle on scale pad 2. Second weigh is TV plus TT no wdh bars hooked up. Have truck the same as first weigh and all trailer axles on third scale pad. Third weigh is TV plus Tt with wdh hooked up. Weigh in same positions as 2nd weigh.
You can now take the first weigh and learn about your tv...take TV GCWR and subtract total scaled TV weight to get your adjusted tow capacity. Take TV GVWR and subtract total scaled TV weight to get your available payload.
Second weigh will tell you about your TT. Subtract total TV weight in first weigh from total combined weight in weigh two to get your total TT weight. Add together the steer and drive axles in weigh 2 and then subtract your total truck weight from weigh one to get your tongue weight. Ideal tongue weight should be 12-15% of the loaded tt weight.
Next weigh 3 helps you figure out if you are setup correctly. The goal is to have your front axle weigh as close to unloaded weight as possible without going heavier. Adjust your wdh to attain this.
First weigh at a cat scale is typically $9-12 and each Reweigh at the same scale in a 24 hr period is typically $1-3. When asked first weigh or reweigh, answer appropriately. The reweigh you will need the ticket number from the first weigh. When asked for truck number say private vehicle. You might need a long broom handle to reach the button as it is at semi truck driver height.