Well, something is wonky here. It's hard to tell exactly what is going on here w/o a full memory dump, but;
The first minidump you sent me is straight forward stuff,
THREAD_STUCK_IN_DEVICE_DRIVER.
This is usually one of two things, the drivers have a bug in them which causes the offending thread to spin wildly (like a failed test condition or something simple) or the hardware itself fails to respond to a request in a timely enough manner. In this particular case it looks as though the ATI driver is attempting to handle a mode change (possibly changing to OpenGL, don't screw around w/ video card drivers that much so.. *shrugs*).
kd> u ati2dvag!CMMPostSetModeNotification+0x79 -0x10
ati2dvag!CMMPostSetModeNotification+0x69:
bf9f553b 8b4074 mov eax,[eax+0x74]
bf9f553e 8945ec mov [ebp-0x14],eax
bf9f5541 8d45cc lea eax,[ebp-0x34]
bf9f5544 50 push eax
bf9f5545 ff159c05a1bf call dword ptr [ati2dvag!gCMMcalls+0x5c (bfa1059c)]
bf9f554b c9 leave
bf9f554c c20400 ret 0x4
bf9f554f cc int 3
kd>
These look like the latest ATI drivers...
kd> kd> kd> lm t m ati*
start end module name
bf9d3000 bfa15000 ati2dvag Tue Feb 21 19:46:46 2006 (43FBDEA6)
bfa15000 bfa54000 ati2cqag Tue Feb 21 19:04:48 2006 (43FBD4D0)
bfa54000 bfa8a000 atikvmag Tue Feb 21 19:11:01 2006 (43FBD645)
bfa8a000 bfd0db80 ati3duag Tue Feb 21 19:30:43 2006 (43FBDAE3)
bfd0e000 bfde0140 ativvaxx Tue Feb 21 19:24:28 2006 (43FBD96C)
f7451000 f75cf000 ati2mtag Tue Feb 21 19:46:24 2006 (43FBDE90)
kd>
If there's a bug in the ATI driver(s), it's possible the Omega's have carried the same bug forward so I doubt they would be much of a fix for you.
The next two are a little more concerning;
DRIVER_UNLOADED_WITHOUT_CANCELLING_PENDING_OPERATIONS.
Both of them have screwed up dumps (usually an indicator of something tromping on memory) and again w/o a full dump it's hard to tell who caused that problem because I can't rebuild the call stack. I'd suggest it's still a problem with the ATI card / drivers because of your scenarios. My first suggestion would be to download some driver cleaning utilities;
http://downloads.guru3d.com/download.php?det=745
http://downloads.guru3d.com/download.php?det=1275
Reboot the system and try installing the latest batch of drivers.
As it also seems to be getting progressively worse and more common in DirectX games as well, it's possible that the card itself is failing. Worst case scenario though.