Ooooh, at highly technical discussion.... When I wrote "tech support do this" I was betting you'd reply "that's me".
"As I mentioned in my blog post, WordPress is installed in the root." -- Showing a list of files doesn't answer the question. Need to know whether DNS gets directly to this folder, or there are redirects needed. You can't (or you're highly technical so perhaps you can but it's certainly a lot of unneeded work) have redirects to this folder and have redirects for domain mapping.
"host does not allow wildcard aliasing" -- a host that gives you command line access, GIT, etc but not wildcard DNS, wow. They probably answered a different question than you asked them. But no problem, multi-site in subfolder mode works.
You have my instruction page, go through all the steps. Quick glance at those images, looks good.
If you find anything different or unclear for your very non-standard hosting setup, please let me know!