One of the reasons they might not want to put the tires on may be the lack of safety beads on your old rims. I would just lever them on myself. Just remember to take small bites, clean the bead of the rims real good, and lube the bead before putting the tire on the rim. After one bead of the tire is on, put the tube in, straighten it out, and pull the vlave core out of the valve stem. Lever on the second bead. Make sure you don't pinch the tube with your tire irons, and then fill the tube with air until the bead of the tire pops in place. Let the air fully escape from the valve stem, and then replace the valve core. Then fill to proper PSI. The shops probably won't have a problem balancing the tire for you. If they do, stick it on the front axle and static balance it the best you can.
