Youve probably already got this fixed but for what its worth, Im with carl.. Bad battery. It may sit between 12.5-12.9, but a battery with a bad cell may read that voltage until you put a load on it, IE starting. A good battery wont drop below 11.2-11.4 depending on amp draw. ive seen some hard to start engines cause the battery to drop to 10.8 and still turn over. Thats where your cranking amps come in. Our engines with an 850-1000 cca battery shouldnt drop below 11.2 while cranking.
A dead cell in a battery can cause this voltage to drop below 5v or lower while trying to crank, and then return to 12.5-12.9 and look like it is within spec. I would put it on a 1.5-2 amp trickle charger over night, and have the battery load tested with a B.E.A.R. ARBST machine. Your local autoparts store should have one of these free of charge. If they bring out a handheld load tester with the little coil and cooling radiator on it... keep on looking.
When you buy a new battery, i would avoid the Optima. Ive owned 3 in both my 10's. They dont fit in the battery tray well, they slide around in it, and the quality isnt what it was years back. Because our battery tray is fairly large, you can buy a larger higher cranking amp battery than what is called for. Just make sure the terminals are on the correct side positive on the left when viewed from the front (series will NOT have an "R" in it), and it isnt more than 1/2 inch taller than the stock one you have. The larger the battery the more reserve and higher cranking amps it will have due to more lead, and more acid.
It calls for a 65 series battery. Some stores will require you to use this battery to maintain the battery warranty in it. If you decide to get this series make sure it has at least 850 cold cranking Amps, 1000 cranking Amps and 150 reserve minutes.