[smarinov]

I have been using precisely Nginx to serve multiple HTTPS domains with certificates from Let's Encrypt since the first few weeks after it came out, so I am not sure why you think it's strictly necessary to assign them separate IP addresses. Generally speaking, there is nothing wrong with that, and it is indeed a somewhat cleaner solution, but it is definitely doable with SNI if one configures their web server appropriately.

Check out the IMHO best TLS SNI test website out there (https://sni.velox.ch/) and the Qualys SSL Labs server test (https://www.ssllabs.com/ssltest/). They may give you a staring point to find out what exactly went wrong with SNI. And the documentation of Nginx, of course.