You have two separate problems then: wandering and side to side sway? Did you have this problem before or after the 19.5" tires? I've read lot's of comments about brand new 19.5" tires wandering a little when new and gradually that issue fades away. If the tires are at proper air pressure they should greatly reduce any tire related sway.
This is just my opinion that I've noticed with car tires. If a tire has deep longitudinal grooves, like most 19.5" front steer tires do, the car will wander if the road has rain grooves cut in the road.