After a lot of struggling and tricks, I installed After Effects 7.0.

But when it starts up it repeatedly states: "Unknown Anti-Alias Policy" and will not allow me to actually use the program.

Any fixes for this? I can't find anyone else with that error, and it seems very few can actually get AE7.0 installed.

As stated at the Wine Application Database, Adobe After Effects 7 currently has serious issues on Wine.
So if you really need to use that program, I would recommend to use it on Windows.

I get that but I really -HATE- using Windows, and don't currently have a partition for it.
It seems I've got a bit farther than the other two entries, as if I could get past this persistent little box warning it seems the program would work, as it appears to load.

What handles Anti-Aliasing by default when you run wine?

You don't need a partition to install Windows, you can use Virtualbox for that.
I don't know for sure, but I think anti-aliasing of drawings on screen is either handled by the GDI(+)-sub-system, or (and I think in your case more likely) by a application-specific function.

Just my opinion, and others may see this different: If you don't want to work with Windows, and Wine doesn't support your Windows application, search for an alternative application that runs in Linux. If you have to use the Windows application, then you have to swallow the bitter pill and use Windows.

I did try a few but none of the programs are half as easy and qualitatively comparable (sadly. It would be great if open source applications were more like GIMP, for example, which I prefer to Photoshop).