Mil-spec shipboard cable can easily handle those temperatures and conditions. Unfortunately, NEC is silent so far as allowing them in structures, but they exceed code in every way and I'd bet your local local building inspectors would allow use if you ask up-front.
I think you need to talk to the manufacturer for as clarification on the instructions. I looked on the web site and I am not sure which light you have but the 125c part can't be far from the ballast. You should be able to use THWN for the circuit conductor beyond the hot spot.
I guess it depends on the box. It this point we are just shooting in the dark. I think you need Hadco to tell you just exactly how you are supposed to install these things. It is their labelling that got us here in the first place. As in inspector I would certainly try to find a solution that didn't require you to come up with a spool of "Unobtainium" wire.
This thread raises an interesting question about a wet location rating.
Normally any underground location is considered a wet location.
But if you have a heat source that can actually heat the wire up to 125C, then it is quite unlikely that the wire will actually be wet In essence, the wire will be baked dry by the light.
So is this a wet location or not? It might very well be wet when the light is off, but dry by the time the temperature exceeds the wet rating of the wire