I am planning a major overhaul of a well established domain (60 Moz DA). Aside from a platform change, content reduction/consolidation and branding update, the structure of the site will be drastically changed. To me, even with redirects, this in itself is a major SEO strain on the site. I anticipate 6 months recovery time before everything is back to normal.
Would it make sense to do the conversion to https at the same time or should I do it in phases?
Do it all at once.
A https switch is not going to impact you more or less if you're changing all the content. A new index will be built and crawled for your site - and your old 301 redirected URLs will be merged into the new index entries.
In addition to this, because the benefits are long term, the earlier you do it then the sooner you'll benefit.
Redirect handling in Nginx has two flavors: for each legacy domain you need to create a vhost if you want to redirect to a deeplink. Servername aliases can span multiple domains, but the return always points to one server (handling the request variable). https implies dealing with the certificate requests and such for all old and new domains that you need to take care of.
Most of the work is done 'after the slash', but using a simple map file in nginx you can translate thousands of stale links into working deep links, and do so efficiently.
http vs https is a non-issue at this level.
So, if you can cope with the crypto, then go for it now.
