It's getting even more baffling. I'm consolidating it all now to repitch. I've dumped about 30 bottles and came across one random bottle that was fully carbonated and about five that let out a really small amount of gas. I tried the shake and dip method with no bubbles as far as I can tell, good idea though.
I don't think it's the bottles or caps/capper as I bottled another batch the following day and those are fine, and it's a quite random assortment of bottles with some grolsch bottles mixed in there. There is indeed a considerable amount of yeast at the bottom of every bottle, so I'm gently mixing it in before dumping. I'll pitch new yeast, let it sit in the fermenter for a couple days, prime and bottle.
This is really getting to me...pdxal might have it with yeast that's too old as it was sitting for a while.
I think the one carbonated bottle was a warning and gift from above, because I actually didn't pour myself a beer before starting to dump all the bottles...
UPDATE: I'm going with providence...as I completed the beer that was carbonated, shortly before finishing the dump, I found another carbonated one to drink.