I have great news for anyone that has a Rhodes being used with a keyboard stand!
I have this kind of stand:
http://accessories.musiciansfriend.com/product/On-Stage-Stands-Pro-Platform-Keyboard-Stand?sku=450384. At first I really didn't like how this stand was holding my Rhodes. It looked like it was sturdy, but when the Rhodes got bumped and slipped off the stand, I knew there was gonna be some problems. Now, Ive finally found a decent mod that makes it much more sturdier. Just mount the stand to the bottom of the Rhodes! On the bottom of the piano there are some little metal foots that screw into the wooden bottom, and on the stand I use there are little cutouts in the frame (I don't know why they are there but I thank God they're there).
Just unscrew the two back foots from the Rhodes and line up the stands cutouts with those two screw holes, then screw the foots back on with the stand frame in between the bottom of the piano and the foots so the stand frame is nice and snug and mounted permanently to the piano. It wont slip, and it will be almost as sturdy as the original Rhodes legs. I even have mine set up in the old "stand up position" right now! This minor mod helps so much. Try it out if you have a stand like this or something close to it!