Rename the module to something like Apache::ASP::Old or similar.
Make the Apache2::ASP in CPAN, a module that when loaded warns about the future changes, telling the user to use Apache2::ASP::Old or to try the new development versions. Then load Apache::ASP::Old so nothing gets broken at this point.
Release development versions using 2.xx_xx version numbers that are not automatically installed from CPAN.
After a while, when the new version is stable enough, replace Apache2::ASP with the new version.
Comment on Re: Releasing a module with breaking changes