If no-one else in the Forum can give you advice more quickly, perhaps my husband can help for other trips - he is now over at Bülach (swimming coach - competition).
I am very much out of date with biking terms - for me a racing bike is tyres with no profile and drop handelbars and no junk such as lights, luggage rack.... My heavier bike is called a city-bike here but it also goes on the road...
I'll give Kurt your post this evening, then perhaps he has an idea for another time. He often goes towards eastern Switzerland a bit (we live in Wädenswil on Lake Zürich) but although he is pretty fit, he is nearing retiring age and carries too much weight so not quite in your league with the 20 Km steep climbing.
His comments in the first post about taking the train were in light of his experience with other folk who come here from flatter countries and who really aren't used to distance plus steep climbing.
Hope all goes well tomorrow.