Debian is upstream for both Ubuntu and MEPIS, but Ubuntu and MEPIS are
independently developed, meaning what MEPIS chooses to include and what
Ubuntu chooses to include are radically different. You cannot expect Ubuntu
to fix AntiX or vice versa just because they share the same package
management system. MEPIS is based on squeeze (Debian testing) and Ubuntu is
based on sid (unstable). You can't even mix the two on Debian itself without
problems, nor can you use Debian packages on Ubuntu or MEPIS without
destabilizing or wrecking your system.

Linux is different from Windows because of the way shares dependencies and
has no registry. This means for your system to work that everything that
shares those dependencies must be from the same source. Mixing sources is a
recipe for disaster. Do it at your peril.

My opinion for what it is worth is to replace antiX with a lightweight
Ubuntu derivative such as Lubuntu and then you can use Ubuntu's huge
repositories. I have nothing against antiX, it is just a simple solution to
your problem. Ubuntu has the biggest repositories. MEPIS as good as it is is
limited by comparison.