There's an easier fix, if this is a problem for you. Just state that damage from regular gear – i.e., not based on superpowers – cannot employ Double Damage if its basic damage wouldn't have hurt the target.
Yes! And this isn't even a "fix" since it's already fully included in the rules with the "The GM has final say on what stunts can be used for" rule on page 81.
Right now, the issue comes from Double Damage applying before armour, which lets low-tier weapons get past protection they arguably shouldn’t be able to affect at all.
This is still trying to solve for a problem that doesn't really exist. As I mentioned before, the game rules need to be taken into account holistically and not piecemeal. To go more into what I mean, let's consider a couple of scenarios during play.
First, if I'm a PC, then it would be unbelievably frustrating if my GM put me up against enemies that I couldn't hurt under any circumstance (unless it was very rarely, and then only where I / the group would need to figure out a vulnerability for the foe as part of a story point). So even if my attacks with a single success (like say a basic Blast) couldn't hurt an older Viltrumite, I would still want there to be the chance that I could do something if I got lucky enough to use the double damage stunt.
This would come down to the idea that as part of the game, the GM would be running it in a way that wouldn't have the PCs regularly going up against enemies they couldn't affect - because what would be the point and that wouldn't be any fun. So the current rules support this better, without requiring all kinds of tweaks in the other direction.
Coming at it from the other direction, why would the GM put the PCs up against enemies that can't hurt them at all? If there's no risk whatsoever, then the GM might as well just narrate "You stand there and their measly bullets bounce off you, then you swoop through and murder them all." Because there would be no point to play the scene out in the game if there's no real chance for failure. But, even if the GM wanted to throw in a scene here or there to allow the PCs to feel really powerful by being entirely unaffected by the fire from a group of soldiers, then they can still do that with the rules as they are - by simply invoking the one I mentioned on page 81 above where the GM has final say on what a stunt can be used for. This is a clean way to handle those - what should be - exceptional and rare situations where the GM wants the PCs to feel like gods with no risk, but it maintains the default framework where there is risk involved in all the action scenes.