I'd try the above recommendations. You might be able to get them under 50 with enough work. There is a -10% LD bonus in the espionage idea group that might be worth taking temporarily until you can incorporate them, it will be a huge waste of DIP points but as you have nearly 6000 development in 1444 it's not exactly going to cripple your nation. Combine that with diplo rep advisers and taking as much other dip rep as you can from other idea groups, and you might be able to get them under control by 1540 or so.
If not you can start back at 1444 and release them day one, then slowly reincorporate them. It will take several wars, but on the plus side if you have the traditional Roman Empire borders you should be able to take 100 WS every time without worrying about AE too much. Nobody is anywhere near Burgundy, there should be only one or two other catholic nations, and nobody is going to have french culture.