Windmill Start and APU....
The best speed for windmill start for the CFMs is 300 KIAS....and 280 KIAS for the V-2500s. Once you get slowed up toward green dot, the only hope you have for an in-flight start is to use the APU. (I suppose it's possible to do an air start at green dot.....just not likely.)
If you're going to start the APU, you must wait about 45 seconds after the RAT deployment (if my memory serves me correctly), to ensure the RAT is up and on line. Starting the APU while the Rat is starting to do its thing may screw up the RAT coming on line. (All this is on the paper checklist.)
Yes, attempting to start the APU will deplete the battery power, but the issue is not electrical....it's powerplant. You want to get at least one engine started. If you don't have enought altitude to push the nose over to get sufficient speed for an airstart, you have no choice but to use starter assist.
Fly Safe,
PantLoad