We use Atlassian Cloud and we have users from two separate domains (both using G Suite). We don't host our website for one domain but we do for the other. We do have control over the domain records, though. Have you considered providing TXT record verification (similar to Amazon SES)?
Our public websites are also not running SSL so no HTTPS there. For us to use HTML verification we would have to setup subdomains just for this purpose. Issue again is that only one domain uses a wildcard SSL cert. The other is static for one URL (www.OURDOMAIN.COM).
I'm not clear on how to proceed. HTML validation might be problematic.