Well if that's the case, I would seriously just show up with my original confirm numbers at the original times -- think of it this way -- what if you had not called to check, what would you have done? Probably you'd have shown up at the times you had written down, with your confirm numbers, right? And you'd probably insist that yes, you DO have reservations, because here's the confirmation numbers...
So why not do that anyway? If you're polite, but insistent that you do have reservations & their system must be glitching, my guess is they'll put you into the table line up just as if none of this had happened...