Galen,
Wine may not be the problem at all, since we have no idea what video card you are using, it could be as simple as that (not enough dedicated video memory...) or driver version, etc. Let's start with which video card and / or the equivalent of dxdiag system information discovery text.
AH2 uses CPU to do its magic as where AH Beta and upcoming new version will use video card in a much more demanding way. I think the low end of graphics cards is somewhere around the nvidia 6800 GT.
