It is my impression that when a vowel comes just before a palatalized consonant it is raised higher in the mouth. "а" becomes almost "ай", "е" becomes "и" etc. Am I right?
Hmm. I am not so sure.
"The store was so far away." would work as a response to something or as an explanantion why you did not go there, but not as stand-alone sentence in English. In general so ≠ very, it's more of an emotional amplifier, and as such requires an appropriate context.
So ≈ так/настолько.
Meantime очень=very, quite literally.