you might have to splurge for this one. there don't really seem to be any budget priced headlamps that can do what you need and do it reliably.
i would think a Spark ST6-460NW with the frosted lens would work well for your application, but if you're committed to AA batteries, i'd get the Fenix HP11 and apply some diffusion film to the lens.
a pure flood like a UF H2 probably won't work because even on max, you're not going to be able to see much of anything beyond 20 feet. i used to have a modded headlamp with a bare XPG that was dialed up to about 150 emitter lumens and it was still less useful for hiking than a 27 lumen Fenix E05. i just couldn't see anything past 20 feet with it.
A Zebralight H51f or H51 with some diffusion over the lens would do what you want (it's what I use) but it's 1 AA. It's simple to change the batteries even in the dark just by touch so you could carry the other batteries in your pocket rather than on your head. It's over your budget however.
As was mentioned it's hard to meet all of your requirements.