I'm not sure that this was mentioned in the episode but -- there actually is a Heaviside Layer. The Kennelly-Heaviside Layer, to be exact.
Apparently this layer is reflective of radio waves, and bouncing these waves off the sky makes it possible for them to reach beyond the horizon.
I suppose this could mean that sending a Jellicle to the Heaviside Layer for a new life could literally mean just sending them into the stratosphere so that they'll land somewhere far away, thereby beginning a "new" life?
The layer was discovered by British physicists in the 1920s, which is around the time Eliot started writing poetry, so odds are this was a word he overheard at a tea party sometime, and 20 years later, he used it in his cat poems.
EDIT TO ADD: the dumbest thing about this is that it was named for the guy who discovered it -- Oliver Heaviside.