We ran a 12x20" cornhead (non chopping) on our 2388 part of last fall. I was amassed at how much harder it pulled than our 1083 even though you're taking the same width of swath & not running a lot more grain thru your machine, but a lot more trash. In 200+ bpa corn we could easily run 5-5.5 mph with the 1083, with the 3212 the best we could do was 4mph.
You'll need a 3rd hyd cylinder, at least weights on the rear weights on the rear, and probabaly fluid in the rear tires. Also duals on the front though we ran ffloaters. We didn't have fluid in the rears & you had to be careful when you pulled the hydro back or you'd set it on the nose.
My personal opinion is your 2366 would have a tough time handling a chopping 12x 20 head. I wouldn't have wanted one on our 2388. There's a guy over on Redpower that runs 12x20 nonchopping on a 1660 & says he runs about 2mph.
my gut feeling is that the whole package would be too heavy for the machine regardless !!! Only problem is, there aren't too many small chopping heads out there. I guess we should have bought a 2388 instead.