You could hold off on alignment too. The big killer of tires is toe. If the pull isn't too bad, you could live with it. If you do go to another shop, tell them you have a front end that requires shims and that you had a less than satisfactory experience elsewhere. Ask them if they can check all the bushings/pivots so that you can replace what is necessary, and if they will do a proper alignment with shims to get your caster, camber, and toe in spec. If they say anything but yes, look for a different shop.
Places with hot rods and muscle cars sitting in the lot are usually a good place to start. Most older cars are aligned with shims. Fun fact, the old jaguar e-types (independent rear) used the rear axle shaft as an upper control arm. The camber on the rear wheel was set by disconnecting the axle and shimming it