Two thoughts have come to mind.
One - are these the factory tires? I recall putting four General's on my Nissan King Cab, they were one size up from stock, stock size was 10.5 x 32 x 15 (I think that's what they were). I too was having a serious balancing problem. Either way the regional factory rep changed out five tires before he eventually refunded my money.
Two - Quite possibly with removing the tire from the wheel should show bermishing of the wheel at the bead area. But without a doubt if you were to remove a wheel from the vehicle and deflate the tire you should be able to unseat the bead from the wheel.