Holy cow, you're absolutely right!
I installed 2.2.3 (removing 2.2.2 first and doing a clean install just to be sure), and Eureka! It works again!
I can now use PHP 5 without issues. CB and Acajoom registration and confirmation work without issues. And I no longer need to have custom redirects for / and /index.php. JoomSEF correctly redirects these on its own to my home page.
As a side note, I exported my jos_redirection table before uninstalling and then imported it again so as not to leave any of my old redirects undefined. I probably wouldn't have needed to do so if I did an in place upgrade, but I wanted a clean slate.
Happy Thanksgiving!
=)