there are super small ac/heat units available to fit street rods [think 33/34 ford] that might be something to consider.
however, you will do yourself a favor by temporarily re-installing your dash to get some critical measurements of the available space you have.
don't forget the wiper arm space needed. [i can't remember if the 62-64's had the arm mechanism under the dash or not. [sorry, "old timer's disease" caused by lots of spiders filling my old noggin with cobwebs. ]