Ahh yeah, 1366 x 768 is definitely an odd resolution and I don't even see that one listed in the EQ options when I check for video modes. I do see 1360 x 768 though.
You may want to try editing your eqclient.ini file directly and adding the section below if it doesn't already exist and then maybe try adjusting the values there to see if you can find a resolution that works for you.
Code:
[VideoMode]
Width=1280
Height=768
WindowedWidth=1366
WindowedHeight=768
FullscreenRefreshRate=0
FullscreenBitsPerPixel=32
You should also be taking a look at your everquest \logs\dbg.txt file to see if it has any useful info related to the crash in there. You can post the output of that file if you want and maybe someone here will find that useful to help you find the issue.
Some other config lines for eqclient.ini that you might try messing with are the sound one (I would recommend trying this as false):
Sound=FALSE
You might try setting this one to 1 (default is 0):
DisableWestBugFix=1
Don't forget to try setting Windowed Mode back to false:
WindowedMode=FALSE