Yeah, I did eventually do all that too. There are 850 nm LED flashlights for night vision devices that give off enough light that you can see a very short distance in front of them. I never did find any 780 nm ones - those would probably have been better given that they'd appear much brighter, but for that reason they wouldn't be popular for the sorts of purposes people would want NIR LEDs for. I've also messed around with lasers at various NIR wavelengths (780, 808, 830, 980) and had some fun that way.
Can you still see something at 850nm or are you seeing some shorter wavelength light that gets emitted by the diode? I did some experiments on my own, but they were limited by the 780nm laser diode which could only be tuned to slightly above 800nm. The visibilty seemed to be dropping off rather quickly beyond 800nm, but that might have been the laser emitting less power at the edge of its wavelength range.
780nm diodes are quite common. Because good laser diodes were needed for CD drives, a lot of optimization went into this wavelength, so that the cheapest and best NIR diodes are usually at 780nm. Maybe nobody bothered to sell them in a flashlight?