I did look at the code, and when I put in an echo JPATH_BASE statement in helper.php, sure enough I was seeing no slashes. Must be some quirk of WAMP/Windows.
I noticed in some other Joomla code that POST is not used to set JPATH. I am not a PHP whiz, so don’t really know why. See index.php in the joomla root as an example. Maybe there is a reason that type of code can’t be used in an extension.