Is there anything I can do to improve handling such as changing out sway/torsion bars?

new shocks is the number one thing

Yep. Hi quality shocks & keep your tire pressures per door jamb specs.
G/luck
Joel

ya new shocks
and this month is shocktoberfest monroe shocks buy 3 get 1 free

Not sure if you can get them for a rodeo or not, but polyurethane bushings help out a lot in other cars and trucks.