Something that can throw that distance and still have a wide-ish flood AND be under $50 is a tall order. Add in a few hour runtime at 300m, and I think you’ll have to compromise on something to be satisfied with the others. You may need to have several sets of batteries to have that much total runtime. Also, you need to understand that making this much light generates a LOT of heat, and most lights will step down from their maximum mode in a matter of minutes (or seconds) to keep from damaging themselves. Lights with bigger heads will be able to absorb more heat and stay bright longer.
Can you tell us what lights you’ve already tried and how they fell short of your needs?
As a general high-power light, I agree with the Sofrin Sp36S suggestion.
Does anyone have throw and lumen numbers for a Convoy L6? (not USB rechargeable, but a spare set of batteries in a USB charger might be a good answer?)