At least two of the tires in the SECOND set of Latitudes did look "egg shaped" as mounted on the wheel. The wheel was fixed fast to the balancer, and the wheel itself appeared to spin very true (confirmed I guess by the Hunter machine at Blacks Tire this weekend). But the tread of the tire tire (two of the Latitudes) seemed to wobble on the wheel as the balancer spun it. There was at least 1/2" of lateral runout in the tread as the balancer spun, with no perceivable runout in the wheel.
I observed what I call the "witness line" running around the base of the sidewall down by the bead. I use this witness line on bicycle tires to make sure I have them seated correctly on the wheel. The witness line appeared pretty uniform all the way around as the tire spun. It looks like any non-uniformity was above that witness line, in the structure of the tire itself. Was this bad enough to cause the vibes in the second set of Latitudes, or was it a poor balance job? I don't know. I never saw any runout issues with the FIRST set of Latitudes. Were those tires 100% okay, and the problem was just a poor balance job? I again don't know.
I can say this, however, with a high degree of certainty. Well, two things, actually.
1. The management of BJs has been top-notch in keeping faithful to me in this process. They've never denied a claim of mine and had no questions with the $100 reimbursement for the balance at Blacks. I went there last night and they paid me $100 in $20 bills at their membership desk. I have zero problems with how they've handled the situation.
2. Having said what I did above, this BJs location seems very unprepared to be in the business of selling tires. They don't always have a tire manager in the shop. They sometimes have only one person working there, so if he's out in the bay and someone walks in to refill a propane tank (which happens quite often), he has to leave the bay and go fill the tank. If you try to call them, they often don't answer the phone (again, because they're understaffed). They only have two balancing machines for their three bays, and one is known to be down (their Coats ride control machine) and their spin balancer (also a Coats) doesn't appear to be working right either. The tire manager last night told me he's had to recalibrate it 4 times since I was there and he's asked to have a new machine brought in. This is very different from the experience I've had at Sam's Club, and from the experience my folks have had at Costco. Sam's always has a tire manager/sales person at the desk to take phone calls or speak with customers, and there are always a number of techs in the bay doing tires. You can walk in at any time of day and have your tires serviced. Because of the short staff at BJs, they ask that you make an appointment.
So while I appreciate the efforts of BJs management to make this situation right, and they have done so, at least so far, I probably won't be buying more tires there. It seems that tires is a "side business" for them, much moreso than at other warehouse clubs, and our experience at Sam's has been much better.