Our last motor home was a on a 1993 E-350. It came stock with a front stabilizer bar but no rear. We replaced the steering stabilizer and added airbags, Monroe shocks, replaced ball joints (your vintage probably has kingpins) and lined it up with only modest increase in handling. It still wanted to wander with some tail wagging the dog
The new coach (in sig) has both front and rear sway bars and a front track bar, it had some wander and really bad tail wagging the dog. Putting in a rear track bar improved the wander and the tail wagging the dog immensely
Now that I know better, I would try the rear track bar before the steering stabilizer, but after getting the worn parts (king pins/ball joints, shocks) replaced and the alignment. Then I'd try steering stabilizer, stabilizer bars and airbags.
BTW, we towed a 2800lb car 4-down, the handling was worse with the toad.