Hey, so I did this trip 8 years ago, so things could be different but I can give a general sense of a few of your questions.
There definitely won't be a bus direct from San Gil to El Cocuy, there really aren't a lot of buses going up to El Cocuy, it's off main routes, 8 years back there was only one bus leaving in the morning from Bogota. I intercepted that bus from Tunja in the morning, maybe 9 or 10-ish. I don't recall the company or exact times, but your route would be probably be San Gil to Tunja, Tunja to El Cocuy. But you'd need to figure out that once-daily bus.
El Lechero was the suggested way to get to the park , the park actually suggested it. There was zero chance at the time that it would be full, it was only me and my friend. If you missed it or wanted to sleep in I suppose you could solve that with money, paying someone with a private car, but the milk truck is probably the cheapest way to arrive, and interesting. I didn't do this from Guican, so don't know if it's the same.
I stayed in cabins and didn't book anything. Generally El Cocuy is pretty far off the main gringo trail, it's hard to include in a loop. There likely are more visitors now, but it doesn't get the same level of backpacker traffic as Tayrona or Salento, or any of the big cities.
You could find a place to store your bag in El Cocuy and grab it on the return (or a place in Guican I imagine). Jan is a good time to go. Anyway hopefully that gives you a bit better sense of things. Bring layers, you will need a good outer shell, rain jacket of sorts. The weather can turn very quickly.
