I've found you get brighter, or you get longer. You don't get brighter-and-longer unless you also accept bigger-and-hotter.

For my lights that take multiple battery types, if I need max longevity (not storage time longevity, but longevity during use), I put NiMH in them. If I need max brightness, I put Li-Ion in them. If I need long storage time, I put primary lithium in them. And I always have a few of those Costco "alkaline 5 bazillion battery packs" laying around for long duration power outages where I wouldn't be able to recharge anything.

Your specific use sounds like you need a very narrow focused beam pattern headlamp (lens) equipped with a corded external battery belt.