Believe it or not, D size alkyline batteries have a capacity of about 20 Ah at low discharge rates. That's almost 10x what you're planning for your rechargeables. Probably the best bet is to look up a battery store in your neighborhood and get a 6V gel cell with 14 An or greater capacity. It'll be heavier than the D cells though. Another option is getting a DC-DC converter to take a more standard 12V down to 6.