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You said you were comfortable with the technical side but I'm a bit of an expert on Drupal SEO and there are some shortcuts. The main one being, use the Pathauto module and the Redirect module. Together, when you change the URL of a node, they will automatically create the 301s. I'm sure your agency would have set that up in the first place. As far as SEO pitfalls for moving content around, you'll lose about 15-20% of the value of any links coming into the old URL. Google doesn't hate redirects but they do discount them slightly. You might use a tool to look at any backlinks you have coming into those pages and contact the webmasters of the sites in question to update them. Tedious but worth it for important links. You can fix a lot of the internal links to the old URLs just by updating the Menu system and any sitewide blocks that you're using (like the sidebar or footer). When I move content, I take the time to buff the SEO of those pages to try and offset any temporary dips in rankings. Often, by the time it's all said and done, the pages actually rank higher than they did before the move. Especially if you haven't implemented Schema.org in JSON-LD yet or set up AMP, both of which have ready solutions in Drupal.

Thank you both. As it happens, just now I discovered the site is already covered with a basic SSL certificate through my host. However, the secure version of the site doesn't load properly - the CSS is being loaded over http, so I need to fix that in wp-admin. Just leaving this here in case it ever helps anybody else! http://stackoverflow.com/questions/27727003/website-homepage-loses-styling-when-ssl-forced

OK I gotcha now. You can submit the sitemap in all versions of Search Console, won't hurt anything to have it referenced in multiple profiles of SC. Another thing you can do to make sure crawlers find your XML is add this line to your robots.txt file: Sitemap: http://yoursitecom/sitemap.xml