First of all, thank you all very much for the help and suggestions you've provided me thus far.  Here's where I'm at now:
'98 GS with 5,500 mi.  Starts fine, idles fine at approx 1,200 rpm until she's fully warmed up.  Then she idles at no less than 3K.
Carbs have been cleaned.  Cracked boots between carb and engine have been replaced.  Idle mixture screw does not change it for anything below 3K.  It can get it up to 5-6K but will not get it lower than 3K.  Throttle cable doesn't seem to be an issue.  Choke cable doesn't seem to be an issue.  What's my next step?

You still have a lean condition. The screw/knob that hangs between the carbs is  your idle speed  not a mixture  screw if that's the "screw" you are referring to.

Define  cleaned your carbs.... Removed-inspected -cleaned the pilot jets-mains etc...( could see daylight through the pilot jets). Cleaned all the little orifices in the carb body-blew them out with compressed air.
New Orings under the carb top caps...new float needle/seat-orings etc in there.... Float height checked/adjusted if needed?

check your gas tank and fuel filters for rust, you may have repluged your jets already if it's too bad. this same thing happene to me and I repluged the jets within 5 miles of running after cleaning the carbs.

Tight exhaust valves can cause hanging idle. When did you last check the valves?

Check the throttle cable again.It maybe out of adjustment and not allowing the carbs to close all the way and return to idle.

Ok. What's involved with checking the valves? That may be a little beyond my scope.

http://wiki.gstwins.com/index.php?n=Maintenance.CheckValves

There is also a video link there that shows exactly how to do the valve check and shim replacements.

Quote from: ben2go on July 06, 2011, 08:59:00 AM
Check the throttle cable again.It maybe out of adjustment and not allowing the carbs to close all the way and return to idle.

This. Completely detach it from the carb, and route it outside the bike so you can rotate it in multiple directions and pull it in and out to make sure it extends to it's maximum.  Or, warm your bike up, drive back to your designated work area, detach the throttle cable, and start your bike.  I had the exact same problem and it was that my throttle cable was stuck.