I have been part of a similar transition on a moderately high traffic website, although with a difference: all of the URLSURLs were changed and no 301 redirects were put in place.
I monitored closely the impact on Google rankings for roughly a month, and for most key words, 2-3 positions were gained, although I'm fairly certain that was completely due to better SEO.
I couldn't see any change that could be reasonably attributed to httpsHTTPS only.
Your plan seems spot on, although I'm a bit torn about that second step, I'd personally go straight for 301.
Why not A/B test with a small number of preferably fake questions and check the effects on those?