I don't have a Thunderbird but I use a stand like this and has done me proud on many machines. http://www.ebay.co.uk/itm/1500LB-Mo...360214?hash=item58b0bdf196:g:d2cAAMXQyFFTkjYa
This is the one I have, it only works if your frame goes under the bike. You can wheel it around carefully. Good thing is you can get it so wheels are well off the ground or both touching ground, I was able to adjust it so there was no pressure on rear springs so I could change them with no effort, yes it's heavy but it folds up nearly flat, about 5" thick for storage. View attachment 7297View attachment 7298
If thats the case then I know a lift called EASI RISER is another option it can lift from wheels, footpegs and frame, various attachments aid this, its not a cheap lift but an excellent piece of kit, lifts with a socket on a drill
Is it possible to make a timber spacer between the bike frame and jack? I've got a bike lift that I use on my America and my young nephew brings his Harley Fatboy to my shed to use my tools etc. we made a spacer block to clear his pipes and it works well.