Well, after some research, the general consensus for regular Cories is about 10 gallons. Given my tank's abnormal depth and the fact that it is only 2 gallons under the minimum, I think I would be able to get away with it. Pygmy cories would be preferable but if I can't find them then I will go ahead with the regular ones.
+1 to Crowntails. The larger cories are more active and, well, much larger. Seriously, my oldest peppered cory is an absolute leviathan. Pandas are the absolute largest cory you would want to get. If you can't get pandas or pygmys, I really would not get cories at all. I don't even like 'normal' cories for a ten gallon.