I just wanted to let everyone know I was having the same "Black Screen" character login problem, however, I fixed it very simply.
After trying to install all of these different things for directx, etc. and modifying native vs. builtin, I found something that made it start working.
I had to manually add the key "Direct3D" and then add this string to the registry "useGLSL"="enabled" in
HKCU > Software > Wine
which ends up being HKCU > Software > Wine > Direct3D > useGLSL=enabled
After adding that, FFXI started working perfectly. Here is all the software that I installed prior, if someone wants to try to recreate my success:
CrossOver HTML Engine
DirectX 9
FFXI
FFXI: expansions
Microsoft DirectX Runtime - Modern
Microsoft XML Parser (MSXML) 3.0
Core Fonts
Also, for reference, I'm using the newest generation of MacBook Air, and the performance is near-perfect, very little lag/slowdown.
Hope this helps people.