As far as I know, the strake first appeared on Westland Sea Kings in the Falklands crisis in 1982. It was a single strake, and resulted in improved tail rotor margins with a right side wind (encountered often when the helicopter was moving to the right to land on a deck). US Navy testing on the strake was not done with a lot of rigor and they didn't adapt it.
Later, NASA did some more work on a UH-1H and found that two strakes were better, and patented the idea. BLR picked up the patent and ran with it.
The main improvement is an improvement in tail rotor margin with a right side wind, and a reduction in pedal activity in the hover. Any improvement in payload due solely to the strake was only applicable in the right side wind condition, and this is where the advertising has been emphasized.
The Fast Fin is a beast I know little about technically, but it's obvious that it will improve the efficiency of the tail rotor to produce side thrust. That's going to reduce the power drain of the tail rotor, which might be available to the main rotor, but not to the point of a 1,000 pound increase, except possibly in a very specific set of circumstances.
Hover performance for civil helicopters is normally only presented for two conditions - an IGE hover determined using a fixed collective takeoff, and an OGE hover. Both charts assume takeoff power at the limiting conditions.
If these two devices in combination really did improve the payload that much, you would see different performance charts with the modification. I don't believe there are any new performance charts produced.
I had a short chat with a person intimately involved with the testing of these devices and he intimated that the difference in power required in the hover was closer to 2-3%, but nowhere near 1,000 pounds in payload.