Do you think upgrading to Mavericks and using the App Store edition could speed up the render process and increase the overall stability of SH3D?

I'm not sure Java 7 or 8 runs much faster than Java 6 (I didn't measure it), but maybe the program could benefit of the performance gain Apple promise for Mavericks...

Where you already able to test SH3D on a Mavericks beta?

Not yet. I'm following more Java versions than Mac OS X versions. [;)]

And will todays new 3D Models soon be included in the App Store edition?

I'll wait at least until Java 7u40 is released (still foreseen for mid-september). But it's possible to import the libraries I released in App Store edition too.