Could there be a golden ratio
Perhaps, but a very tricky question I think due to the sheer number of influencing factors. For example do you want the ratio to be golden when the beans are small, green and hard or later in the roast when they are bigger and less dense. The bean expansion paradox. A bit like the problem we have trying to extract meaning from other folks TC numbers, the size of drum and drum contact time would only be comparable if all other factors were the same.
My feeling is that the 'best' performing roaster will always be the one that reacts most quickly to user input. I do not think the drum material(and other factors) affect flavour, it affects the type of profiles available, which affect the flavour. Could be wrong, but once seasoned it seems we are all roasting on a coating of polymerized oil.
Regarding character, again I think this is a flexibility issue, if your roaster forces you to roast in a certain way due to excess mass, inadequate heat, poor airflow etc indeed it will have certain characteristics- that could be easily emulated on a roaster capable of hitting a variety of profiles.
That said I would enjoy seeing the data, and for my part I shall measure the drum on my 1kg next roast.