Binder and Boring solve the mystery of the stone-age Superman in Action 350 (May 1967).
Perry White gets trapped at a cave-in at an archaeological dig. When Superman comes to dig him out, they discover the skeletal remains of a caveman, wearing a Superman uniform.
Superman travels back in time to investigate, and winds up in a prehistoric era, with both dinosaurs and cavemen, and even a red sun.
As far as I understand, the red giant phase is something our sun has yet to experience, not part of its distant past. But whatever, it leaves Superman powerless.
Superman runs afoul of a tribe, lead by Guarr, but eventually proves himself to them. Guarr wants Superman’s costume, which retains its invulnerability. Somehow.
One of Superman’s robots comes back in time, worried that his master has not returned. He brings Superman back to the present, and they leave a costume for Guarr to wear and die in, and be dug up centuries later.
I have to confess, I wish it wasn’t Wayne Boring on the art. Superman grows a beard while in the past, but Boring never makes it look like much more than some shading.
Dorfman and Mooney pit Supergirl against some unheroic Heroes in this story.
The Heroes are a rock band, who dress as Batman, Green Arrow and Green Lantern, as well as a girl dressed as Supergirl. Linda enjoys their music, but they are really a gang of thieves, who steal from the locations they perform at, while everyone is watching their Supergirl.
Supergirl notes the correlation between the thefts and their performances, and goes to question their Supergirl. She has also just figured out what is going on, and wants no part of the ban anymore. When Supergirl shows up to rehearse for their next gig, the boys are suspicious. She seems to be much better than she had been previously, and they suspect she is the real thing.
They lay a kryptonite trap for her, but their pans backfire badly. It was not the real Supergirl, just their singer, pretending to be, so the kryptonite does nothing. Supergirl calls on the Justice League of America, and Batman, Green Arrow and Green Lantern are happy to help her round up the band, while Hawkman sits, stuck on monitor duty.