Jack up front end and give the wheels a good back and forth, top/bottom, front/back and determine if there is any play. I know you said that it is tight, but check again.
In the Southwest if we leave a car parked on a slope or in the hot sun sometimes it takes awhile for the tires to return to round. Works just the same in cold country. Especially if tires are old and dry.
Do as suggested and check pitman arm and all front end components with the car front end off the ground.
OK, I'll join RalphM on the hit list. A stabilizer is a band aid but it is good until your ready to dig into the front end.
Enjoy the adventure, Chap