problem fixed on client's site
In case anyone is interested for future troubleshooting... there was no tmp directory for the client's site, and therefore the sessions were not being saved. My hosting provider added it and now all is working properly on that one.
Problem solved with the Experiment form I was having issues with hosted on the other server. Through the hosting provider Control Panel I was able to edit the ‘session.save_path’ in the php.ini file by giving it an appropriate path to my document root. All is working with that that one as well.
Chalk this up to inexperience. Thanks for your help, Jason - you were really instrumental with these fixes.