Skyhawk1
It is not to operate in Canada, but simply to give the aircraft an internationaly accepted registration. DHC-5s can't be registered in old Europe, so Canada and the USA are the only alternatives to having the aircraft registered in countries like Swaziland or Equatorial Guinea.
Big Pistons Forever
Yeah... Gimmie a double-row radial or nothing...
I'll try to contact these guys in Edmonton.
CD
The A-124 certificate is for DHC-5A (civil) models. Some -5Ds like C-FASY of Yellowknife have been converted from -5D to -5A (civil), however it seems rather tedious as it implies an engines change -- to lower horsepower -1 or -3 engines! The DHC-5E version provided in the A-77 certificate, which fits s/n 108 and onwards, seems much closer to the -5D -- same engines and props, at least. Dunno what the other differences are, though.
Yazman
Public Service out of Anchorage operates DHC-5 s/n 3, so like you say there must be a way to go with the FAA too. As for the NASA one, it is probably considered 'experimental', though...