The 20-gallon tank is the same physical size as the 13.5-gallon, the difference is an internal baffle (so I've been told). If you're buying a tank, get the 20-gallon version.
Don't know if the senders are different. Even if you put the 20-gallon version in the 13.5-gallon tank, it would be better than nothing. It might stay on FULL for a long time, but I expect that 'E' would always be EMPTY.
Just remember that you have a carburetor, and the tanks for the fuel injected models are different.