John,
Your existing tyres are 7 years old and not worn out, suggesting a low annual mileage. It is not unknown for tyres to develop a flat profile if they have rested in one place too long. If this is the case, they will dynamically balance but you will have perfectly balanced 'square' wheels that give an awful ride.
On my '72 +8; each of the holes through which the wheel studs go have a steel insert or sleeve. It is the bevelled part of the insert that the wheel nut centres and tightens against. If the wheel nuts are over torqued the mating surface can split or fracture. If this is the case, the wheel won't pull down evenly and you can get a wheel wobble.
Remove each wheel, inspect each mounting hole to determine that a bevelled mating surface exists. If all is visually OK, remount the wheel and re-tighten with a torque wrench (70-75 ft lbs), if the nut feels 'soft', i.e you are putting the right effort in but the nut still turns, then the insert may be cracked.
The inserts should be regarded as consumables. If the ends of the sleeves are missing or damaged the sleeve can be hammered out and new one inserted using a suitable sized socket as a drift.
If your tyre shop uses an air wrench / chatter gun to tighten the wheel nuts don't expect the inserts to last long.
