Well-known Thunderbird restorer Lance Herrington perfected the first "anti-sway" bars for classic Tbirds and started selling and installing them in the mid-eighties. They've become very popular because they reduce the "floating sofa" effect of the factory suspension.
Visit his website at
www.thunderbirdsouthwest.com then pickup the phone and call him to discuss your situation. He's a suspension expert and can provide you with several options (gas shocks, air-ride suspension with auto-levelling, etc.). Good luck.