“…periodically rotate the position of the batteries in the battery pack…”

For these type of flashlights (actually any item that batteries are in series and there is no circuit tapping off the middle of it), rotating the batteries won’t help. It’s all in the brand of alkaline. If you have this problem, stay totally away from that brand. You can’t afford these kind of failures in the field. Their capacities are all over the place. It’s like mixing carbon zinc with alkaline batteries.

I have seen this problem in alkalines from batteries.com (their own brand) and others.
Also, the generic lithium’s exhibit this problem thus I went back to the Energizer Lithium’s (AA size).

Good luck with batteries.
-Barry