If it gives you peace of mind, go ahead with the dowels. With properly jointed edges, they're completely unnecessary for joint strength, but will help with alignment.
Neither glue will allow you to repeatedly soak the cutting board for extended periods, as they're non flexible and soaking will cause excessive swelling of the wood on either side of the bond, which will weaken the joints. The TBII will work great provided when cleaning, you scrub, rinse and dry minimzing the time the wood has to soak up excess water.
When sanded, use a foodsafe finish (like parafin oil) to help seal the wood and it should be good for several years of use.