SUCCESS!
Well, after all this time, I tried re-downloading the archive. This seemed to be the secret sauce.
After the install, mysql still wouldn't start, so I went ahead and chowned the lampp directory for nobody:root, and started lampp, without running the security.
Fired right up!
Ran the security and boom. Still works good!
Thanks for the help everybody -- and sorry about the hassle, especially for JonB.