JD I copied your two letters and pronunciations into Google and one of the hits on the first page was a link to an extract from Russian for Dummies which said, "Because when it appears at the end of a word, ж (zh) is pronounced as ш (sh). (For more information, flip to the later sections “Vowels misbehavin':.."
You are correct, of course. Final consonants tend to lose their value through softening. D becomes T, V becomes F etc. That was not what I had in mind.