Signed SSL Certificates for server without port 80/443
Solution 1:
I read that LetsEncrypt wanted me to create a TXT record. I was so foolish to think they wanted me to create a TXT file in the root of my public folder.
All thanks to Michael Hampton really, who pointed me in the right direction with 2 simple words: "DNS Validation"
The result:
EDIT:
The following years I discovered how hard it was to maintain these certificates, because they relied on manual tasks (i.e. adding TXT records). And I had to write my own set of scripts to update those TXT records, which wasn't easy.