Seams there are devices made just for this purpose, the one I see most in googling this is called a (Hum X) it’s a filter designed to eliminate ground loop. And what you may want to buy if my above suggested test does prove to show you indeed have a ground loop condition. The links below are some interesting reads on the subject, and point out a potential danger in playing your instrument without a ground long term. The last one has an interesting concept of using a ground fault outlet, wired as if being used in a circuit without a ground wire. Others may comment on that solution and the safety of that. Could a guy make a short extension cord with a two prong plug on one end and a GFCI outlet on the other in a box and get an acceptable level of safety while eliminating the ground loop? That I don’t know. I know they make short adapters with GFCI built in them that have three prong plugs and carry the ground thru.
https://www.youtube.com/watch?v=qBEvnSmXc84
http://www.harmonycentral.com/t5/Guitars-and-Amps/Banish-Ground-Loop-Hum/ba-p/34633804
http://www.epanorama.net/documents/groundloop/problem_solving.html
https://www.youtube.com/watch?v=qBEvnSmXc84
http://www.harmonycentral.com/t5/Guitars-and-Amps/Banish-Ground-Loop-Hum/ba-p/34633804
http://www.epanorama.net/documents/groundloop/problem_solving.html