As I have mentioned in the past, Mort Weisinger operated on the assumption that his readership turned over completely every seven years, and so he had little compunction about swiping stories from that long ago. Here's an example that fits the time pattern precisely:
Action #220 is the September 1956 issue, while Action #304 is the September 1963 issue. Note in particular that in the earlier story, DC was capitalizing on a current event, as 1956 was an Olympic year, while in 1963 the games were a full year away.
The stories are very similar as you can see from these opening panels:
On the next page, things do diverge a bit; in Action #304, Lana Lang happens along in her helicopter and is pulled into space along with Superman, whereas in Action #220 Superman travels alone. There turns out to be an important reason for this difference.
In both stories, a scientist from an alien world has sent out the attraction ray to bring Superman to his planet for the Interplanetary Olympics. In both stories, the prize is the same:
That's rather interesting in that one of the promises of nuclear power back in the 1950s was that it was supposed to be ridiculously inexpensive; in fact the claim was that it would be too cheap to bother metering. That certainly didn't prove to be the case.
In both stories, Superman performs very poorly:
But Weisinger (and writer Leo Dorfman) do have a substantial change in Action #304 to the Action #220 ending (tentatively credited at the GCD to Edmond Hamilton). In the original, Superman discovers that the top contestant, Bronno, is a robot, and that the reason for his own weakness in the stadium is that a block of Kryptonite was used in its construction.
In the revised version, Superman was intentionally losing, because he caught onto the fact that the games were rigged. It turns out that the contestants and the scientist who had brought him to the alien world were actually crooks, hoping to tap Superman's powers and use them to evade the law. Naturally, Superman didn't intend to help them, and in fact the story ends with the interplanetary police arresting the trio.
This also reveals why Lana was brought along with him. In the original, Superman was puzzled by his own weakness, but with the revised ending Lana had to be the one expressing surprise. Note in particular that in the panel where Superman's climbing out of the water, that he carefully avoids lying. "I'm doing what I can," not "I'm doing the best that I can."