Stop in for a cup of coffee

My parents had something similar and no, there’s really not much a steering stabilizer will do on that since it’s not got a solid axle under the front. Not sure if they make them for 2wd. On a solid axle, there is a bracket on the axle and then in the tierod link.then it uses a shock or two to dampen road vibrations.

If it’s swaying as bad as it sounds, I’d check the rear sway bar, should have one factory in that year. I’d bet the bushings are wore out.