I have run my '53 on 16s since I bought it and use Avon Tourists with them. Although it's not the greatest handling car in the world, everyone should remember that these are OLD cars and as such won't handle as well as later more developed 356s. Please note I drive this car a lot and have been into Europe a few times with it (am taking it to the International in Switzerland in May), the car just takes some getting used to.
From what I've been told, if anyone is running with 16s then it is important to have the car set up exactly right as they are quite sensitive.
Graham, let me know if you want to dispose of any of those rust old wheels!
