Twill weave is very similar to plain weave. It should be a little bit stiffer and stronger but in practice it may not be, because a lot depends on the volume fraction achieved, although often plain and twill have almost the same volume fraction. See
for an example of plain and twill weaves (the E and σ are very representative of the differences between them). Often, as there, the twill weave is produced with a higher areal weight, although in your case it probably isn't (200 gsm is pretty light for woven material). The areal weight mainly affects the thickness (which of course determines the sort of strength and stiffness you get for a given amount of carbon). For carbon/polymer with sensible volume fraction (about 55 or 60%) you can take the areal weight in gsm and divide by 1000 and that's the approximate thickness in millimeters.
The only time you'd need to model the difference between plain and twill is if you were investigating the meso- or micro-mechanics, where the weave featured in the model. As it is you should be modeling the material with its in-plane (and through-thickness, though this can largely be ignored with sandwich) properties, whatever they are, and those numbers should be almost identical to the plain weave numbers.
Are you modeling the flat elements as sandwich, or are you modeling the skins as separate elements from the core? Again, twill vs. plain won't make any difference. Just curious about your approach.
If you're using sandwich panels with right-angle joints it'll be quite interesting how you achieve that. It has been done with (e.g.) the Beech Starship's wing skins and ribs, but that was mainly for a shear connection (the wing wasn't wet to there was very little tendency for the wing skin to be pulled off the ribs). The fuel was in bladders in the center wing box and the inner wing.
That thingummy in the illustration looks like a bathtub tension fitting, not the sort of thing usually made out of sandwich panels, especially since it looks like it may have significant pull-off loading of the joints...