Wow, 2.5A from alkalines is probably not doable. If it is, it's not safe.
Given your need for high current in a small package, I would eliminate alkalines from your list of options. If operating cost is secondary, 1.8V lithium AAs would be a sound choice. Even if you want the freedom to switch-hit between rechargeable AAs and primaries, make lithiums your primary cells. You can find them now in any drugstore.
As for your rechargeable AAs, the default choice would be Sanyo Eneloop NiMH: they'll deliver high current without voltage sag. But if it's 6 volts you want from 4 cells, you sound like a perfect candidate for the new "green" 1.6V nickel-zinc rechargeale AA cells. Like Eneloops, they hold their voltage nicely under high loads. Their main drawback is that they require a special charger, they aren't safe to leave in the charger overnight, and that they have only about 75 percent as much amp-hours as Eneloops.