I think it depends on how much of the original you're using. If you were just inspired by it to write a story about the Rye House Plot, that's one thing. If you're using the same characters, same plot, same situations, and lifting the dialogue, that's another. Once something has fallen out of copyright you can publish it at will, quote it without permission, use the characters in new situations, etc.--but what you can't do is copyright, under your own name, the same material.
Here are a couple of pertinent quotes from the U.S. Copyright Office:
To be copyrightable, a derivative work must be different enough from the original to be regarded as a “new work” or must contain a substantial amount of new material. Making minor changes or additions of little substance to a preexisting work will not qualify the work as a new version for copyright purposes. The new material must be original and copyrightable in itself.
And:
One cannot extend the length of protection for a copyrighted work by creating a derivative work. A work that has fallen in the public domain, that is, a work that is no longer protected by copyright, may be used for a derivative work, but the copyright in the derivative work will not restore the copyright of the public domain material. Neither will it prevent anyone else from using the same public domain work for another derivative work.
So it sounds like a total rewrite could be copyrighted, but any chunks you pull from the original would not be. Plus, if someone in Hollywood wanted to make a movie out of it, they could bypass you and head for the source material, and there isn't a darn thing you could do about it.
If you're really serious about it, your best bet might be to talk to a copyright lawyer, who could help you determine exactly how different your version needs to be to be able to copyright it.