I have the same card and the same problems (that's how I ended up here). I'm afraid there is no desktop effects until Amd fulfills its promises on the matter, that is, until they reveal critic documentation on their newest cards (they have already revealed it partially) and/or develop the new propietary drivers for linux they are supposed to be working on right now.
By the way, are you talking about the "ati-driver-installer-8.40.4-x86.x86_64.run" package? I have just downloaded it, but I don't know how to install a .run file,
Anyway, have you tried with envy or other scripts to install the drivers automatically (automatix, easyubuntu, it seems that I still cannot post URLs sory)? I'm with the beta of Ubuntu 7.10 right now, so I'm not sure if I should use them.
Finally, about the resolution issue (do you have an LG204WT too?) open /etc/X11/xorg.conf and look for the "Screen" section, you just have to write all the resolutions that your screen can bear in the same format and save the file. Reboot the graphics server (did I say it right?) and voila.
EDIT: I've search for the situation on ati drivers and, how do you know? there are already linux drivers that support AIGLX (yes, beryl and compiz for everyone) since mid-September: the 8.41 drivers. For some reason, the drivers you get from ati are the 8.40, o_O, but you can get them in softpedia
. It's another .run file so I still have no idea what to do with it,