JimmieC and others...for what it's worth. Way back when the DR100MKii first came out there were a few of us that ran across this issue of short run time off alkalines, but it was only when trying to power mics with phantom. As you've discovered the runtimes are much longer from batteries with zinc and lithium chemistries.
What we figured out is that the alkalines discharge at a slightly lower voltage than the lithiums or zinc rechargeables (at least along the flat part of the voltage discharge curve). Apparently, when the unit is pulling max power when phantom power is on, the draw is enough that it pulls the voltage down on the alkalines low enough that they reach the low voltage cut out on the deck within a short time...it's only like 30 or 40 minutes even with new alkaline batteries. The batteries aren't necessarily dead, but they will no longer power the DR100MKii. If you power the deck from the internal li-ion, this doesn't happen until after the li-ion goes dead and power switches over to the AAs.
With zinc and lithium chemistry AA batteries, the flat part of the voltage curve is a little bit higher. Since the cut out voltage is still the same, it's apparently just low enough that it stays below the flat part of the curve on those types of batteries so that you get much better runtimes before reaching the low voltage cut out.
We gave this feedback to Tascam way back on Day One and asked them if they could look into a firmware change of the low voltage cut out point, but Tascam customer service being what it is, the request was never responded to and this issue was never addressed.