Larry:I am planning the exact same swap on my '55, however using a 1960 COM with the later '61/'62 aluminum bellhousing. The '60 COM still relies on mechanical linkage to regulate the internal line pressure. If you are only replacing the tranny, you will need to swap everything from the flexplate back. I belive there is only about 9/32" overall length difference between the FOM and COM (medium case). You will need the tailshaft yoke, but the mount, driveshaft and crossmenber should be fine as will your cooling lines and radiator cooler. Your '61 tranny should have a vacuum modulater that controls the shift pressure chores so this should simplify your bellcrank/linkage problems as you only have to contend with the kickdown function. Your existing 4bbl linkage should work fine. I'm not sure you'll find a COM indicator lens that will fit and function on your '56. The tranny detents as you surmise will determine where the column lever is, however you may not have enough travel on the '56 column to reach "L" on the COM (I'm using an Ididit shifter column). Usually this isn't a big deal.
Let us know how the swap progresses.