you ask about increasing receiver capabilities but I would be concerned about payload capabilities. Have you weighed your truck loaded, ready to camp with all occupants and pets in it plus a full tank of fuel? if not then I suggest going to do so. then take the scaled weight and subtract it from your TV gcwr to get your adjusted towing capacity. The loaded weight of the TT must be less than this. Take the scaled weight and subtract it from your TV gvwr to get your available payload. The loaded tongue weight of the TT must be less than your available payload. The loaded tongue weight of a TT should be 13-15% of the loaded weight.
Do you know for certain how much weight you have added to your Shasta from its dry scaled weight (yellow weight sticker in door or cabinet of TT)? if not then with only approx 1700 lbs cargo capacity on the 319 TT I would calculate using the TT gvwr. The gvwr on the 319 is 9680 lbs. That means a tongue weight possibly as high as 1452 lbs.
the 326 has the same gvwr as the 39 but as a much larger capacity. you are not likely to load 2400 lbs of gear but it s possible. The average camper adds 1000-1500 lbs of gear, some more, some less. You could weigh all of your gear as you pull it out of the Shasta or weigh it loaded and unloaded to figure that weight addition out. If you know the amount of weight added, then you can add that weight to the stickered dry weight (this includes weight of options etc) to get an estimated loaded weight. or you could calculate using gvwr of TT. Looking at gvwr of 9680, you again look at 1452 lb worse case tongue weight. if you know an estimate then it could be less. ie if you knew the stickered weight to be 7600 lbs (random number) and you knew you were to add 1000 lbs of gear for a loaded weight of 8600 lbs, a 13% tongue weight would be 1118 lbs.
I also find it very hard to believe your current TT is heavier nd only has a 650 lb tongue weight. that would mean you were unsafely low on hitch weight. How did you get that weight? did you get it from a sherline scale, a calculation after hitting scales, a dry tongue weight from a catalog or a guess? Have you scaled your Shasta to get an accurate loaded TT weight? if you haven't already, go to CAT Scale
and find a local scale. you can also try a feed store or landfill to find a scale. good luck and happy hunting