Sincerest thanks for touching base so quickly! Your idea is excellent, but my particular situation is tricky: the response was essentially “here are more details to my original story,” so it was essentially a re-hash.
I’m going to take a stab at re-working it though to see if there is another angle I can make work while still retaining enough of its core that the new publication will still be interested in it. My concern is that the whole premise (and what made it appealing in the first place) was essentially the original story. Still, you have given me sound advice and it’s worth seeing if I can salvage this in an acceptable manner to all parties.