MBWD on "Mapped domain redirects and subsite HTTPS issues"

I had a multisite network set up and running successfully at mywriting.network, but needed to change servers, and since then have been having some problems.

Primarily, mapped domains are no longer working. Instead they are throwing redirect errors. I'm using the WPMU Domain Mapping plugin to handle mapping. I've got the normal WP htaccess for multisite straight out of the Codex at the site's root level, but I also have another htaccess doc one level up, in useame/public_html, which reads as follows:

RewriteEngine On
RewriteCond %{HTTPS} !=on
RewriteRule ^/?(.*) https://%{SERVER_NAME}/$1 [R=301,NC,L]

This was added in by the new server owner at my request to solve a previous problem I was having after the server move, when the http versions of all subsites were retuing 404 errors, but the https versions were working. I guess this new rule is probably contributing to the mapped domain redirect error, but I am leery of changing it myself because it fixed the other problem.

And, the other issue I'm having, which I think is related, is that while subsites do come up, their https seems to be broken. They are all saying they're calling insecure images. I can trace the images and change the URL from http to https easily enough, but this was not happening on the old server and it's not a practical solution to go into each and every site on the network and fix each and every image, especially since this issue seems like the symptom of something.

I have two certs installed on the server, one for the main site and one wildcard, and have a dedicated IP as well.

How can I rewrite the htaccess document(s) to prevent the redirect error for mapped domains and allow https to work properly for subdomains?