Hi Rob,
1. Will updating the sitemap for this test have a big impact? Google has already picked up the new URL's so that's not the issue. Furthermore, the 301 redirect on the old pages should tell Google to show the new page instead, right?
No, updating the sitemap won't speed the indexing up (but you should do this as a matter of course), but a 301 redirect should tell Google that there is a new page in place.
2. Is it normal that search impressions will slowly shift from the old page towards the new page? How long should I expect it to take before the new pages are consistently shown over the old pages in the SERPS?
I have asked John Mueller this in the past and he said "as long as it takes - just have patience".
Basically, sit tight because sometimes it can take hours, other times it can take weeks and months.
I would need to be taking a more in depth look to see if there was anything else going on.
-Andy