That's a LOT of stuff for a chest freezer. You're not talking about a $160 7 cubic foot Lowes special
Ball lock kegs are 8.5" round and 25" tall
Pin lock kegs are 9" round and 21" tall.
I don't know the diameter of your gas tanks, so you'll have to figure that out.
Cut out some cardboard discs - (4) 9", (4) 8.5", and one each for your Co2 and Nitrogen tanks.
Take them to Sears, Lowes, Best Buy, etc. and actually place them in the freezers. This is the only way you'll know for sure that your planned system will work.
Remember too, that you can keep the gas cylinders outside of the freezer, gaining you a little more room (Or allowing you to buy a smaller, cheaper freezer)