If I use my HH with cold wind, I use a Thermarest Prolite 4 inside the HH, to prevent cooling by conduction.
I'm looking for another solution, to lighten the weight of the system.
I have not tested the undercover/underpad system, now available at HH.

You can use it as a chair, while cooking under the rainfly;

Snake skins are a MUST : hammock is set-up or packed in a few minutes.

Yes, by all means, choose a big rain fly with the hammock ; or take both the standard and the hex fly.
Last night spent in the HH, with wind turning and blowing the rain in every directions, I get a bit of rain inside, because I had not correctly positioned the rain fly. So, next time, I will ensure a better coverage.
Anyway, a large rain fly will also give you a dry area under which you will be able to cook, to store your gear, ....
Or you can double the fly to better shade the sun ...

My main problem with my HH : I do not have enough time to use it more frequently....