Full Auto is fun. I have had the opportunity to shoot several by virtue oif working with Police. MP-5's, (including the suppressed ones), Thompson, M-16's, etc. Once at a range there was a guy with some tripod mounted belt-fed air cooled thing that was pretty fun, except it was an oldie, and it fed with cloth belts and jammed about every 20 rounds.
There is this huge machine gun shooting festival every year in a place in TN called Knobs Creek, if memory serves. I think that would be worth the trip for you if this is a true life dream.
HB