Dont get to frisky on the tolorances and natural frequency business....
remember your limiting factor will be the seeing which at best gets no better than 1.1 seconds of arc and only on phenomenal nights will you drop below that but its once in a life time event!
Lateral expansion will not change the distance of the primary to secondary hence the reason why its not a issue and in most cases ally will be used for the lateral components and carbon for the length.
As for the primary yes thats what i would loosely base my mirror cell on. This will give you the best structrual rigidity and keep your collimation stable thats in my view.
If you have a look though the two areas on my site Equipment (also look at the top under current projects and in the Image gallery theres another one of my stuff and workings youll see what im using/doing