I was looking for this earlier and just now found it. I really like the looks of this light, and it seems like it may satisfy your requirements:
Fastech also offers the Trustfire Protected 14500 cells for $5.34/pair here:
The FandyFire Rook from Fasttech for $28.90. Fasttech is a newer dealer here, but several BLFers have reported receiving great service from them. The Rook is a mimic of the SkyRay King design, but is specified to run from 3x rechargeable 14500 Li-ion cells, as well as AA cells, so you should be able to use this with off-the-shelf primary AA Alkaline cells and NiMH rechargeable AA cells as well. The light has a single XM-L T6 emitter and a mid-sized 38mm (1.5" diameter) head so it should be somewhat throwy, but not overly so. The light is just over 4.5" long, so well under your needed 6".
This light is on my "to-buy" list, but I do not own it at this time; my 'recommendation' is simply based on what looks like a nice flashlight to me, that may possible satisfy your requirements. I have also never dealt with Fasttech, so I can't recommend them from personal experience. Based on what other BLFers have said here, I would be willing to order from them...
If you buy this light, please post a review here for me!
<edited to add...>
Here's a review of this light: https://budgetlightforum.com/t/-/12703