I don’t think “other” ports are supported in the authentication mechanism - only 80 and 443.
If either of those ports is reachable to any IP in your system, then you could use a catch-all to handle the .well-known/acme-challenge requests via a common folder.
The trick is (two-part and probably unautomateable) [I think I just made up a word!]
- Getting IIS to see them individually - that requires SNI and separation (like my.server:80 is a distinct site from my.server:8888) letsencrypt-win would see the :80 site but not the :8888 site
- Getting the :8888 site to use the same cert as the :80 site.
An alternate would be to use a different client - one that has figured out how to automate IIS and alternate ports.
Maybe this new PowerScript client can help: WAT - Windows ACME Tool