In what do I run high-flying action-adventure?

Savage Worlds.

Dungeons: the Dragoning 40k.

Can you expand on that?

GURPS/Savage World/FATE aside, how about Barbarians of Lemuria?

In a setting like that, a fine elven bow is just another man's blaster canon, so I doubt the fact that the system is technically designed for literal barbarians will be much of an issue.

I'm surprised to learn from this thread that Dungeons: the Dragoning 40 000 is a serious thing and not just a meme.

The sword and sorcery genre is all about sorecerors, cults and unknowable entities they serve.

Face it, youre just wrong.