I haven't tried to tweak contrast and gamma; are you sure they can affect shimmering?
There are many things that can effect shimmering and basically I'm just making suggestions that maybe you could check as anything is better than nothing when one has a desperate problem.
Basically at the end of the day shimmering is when your graphics are too sharply contrasted and normally the AA takes care of that but for some reason in your case its not, so something additionally needs to be done, but what

Ok, I have just fired up my old PC which does not have the problem and has the following specs:
P4 2.6 gig - 1 gig Memory - 6600GTS256 - WinXp Pro Sp3 - Acer 19" CRT monitor set to 85 HZ at 1024x768
The 6600 driver info is as follows:
Provider: NVIDIA
Driver Date: 19/11/2007
Driver Version: 6.14.11.6913
Digital Signer: Not digitally signed
Here I am not using nHancer and everything in the nVidia Control Panel is at default.
FS2004 installed only with Patch 9.1 and Nocd - no additional mods except a few extra aircraft.
Everything set to High and Density to Very Dense with AA ticked on.
Maybe we are missing the obvious and that is the graphic drivers.