David...well that is simply not going to work.
1. Your battery pack is not designed for a deep cycle load...just a few seconds at a time. The 250 CCA (cold cranking amps) that your pack is rated for means it can deliver 250 amps for 30 seconds before being dead flat (10.5 volts).
2. Any wet cell battery BANK that would be able to handle this job should be sized at at least 300ah to handle the 62 amp load (MAXIMUM current should not exceed 20% of battery capacity...62amps is 20% of 310ah's). By going to an AGM battery you could cut in half the size of the bank quite comfortably and if you want to go further a single Odyssey group31 battery could handle this load since it is able to handle current up to its' rated ah's. The price though is quite a bit higher ($300 or so) but it is a single battery and can be recharged at high rates and discharged quite deeply (80%) and still provide good life cycles. The weight is 77 lbs.
Amazon.com: Odyssey 31-PC2150T Heavy Duty Commercial Battery: Automotive
Your actual amp hour usage per hauling will be 7/60ths of the 62amp draw per hour...or about 7 amp hours per haul...so the Odyssey would allow you to do around 10 hauls on a single full charge before needing to be carried back for a re-charge from a THREE STAGE battery charger.
There may be other approaches to powering this winch such as running electric down to a ACtoDC power supply or buying an old jeep and running the engine to power the winch...
... but the Odyssey seems to me to be your best shot at something working reliably. Hope this helps!
EDIT...the Sears Platinum Marine Battery group 31 is the SAME battery as the Odyssey 31 and will save you $50-60 bucks.