You might want to test your battery under load if you haven't already. You may find the voltage drops a bit. Look at the rating on the AC adapter, and try testing the voltage on the battery at that load (probably around 3/4 amp if it only gets 2hrs on a single AA).

Running at 3.6V PROBABLY won't hurt the device. The electronics should be able to handle the higher voltage if they were designed right. It may run a bit hotter, but you most likely won't notice the difference. Adding a diode in series would lower the voltage a bit. Ask the guy at Radio Shack for one with a 0.4 - 0.6V forward voltage that can handle at least 1 amp.

A simpler solution is to create an external battery pack with 2 D-cell batteries. You can buy a battery holder for a couple bucks, and wire it up to a plug that will fit the external power connection.

The D-cells have about 5 times the life of AAs. AAAs, AAs, C-cells and D-cells all have the same voltage (1.5V). The only difference is size and capacity.

Most digital devices are designed to cut off before the battery gets to 1V, so there's never any danger from undervoltage.