The idea with Letsencrypt is that you'd schedule the renewal as a cron job, so the fairly short lifetime wouldn't matter--your server would automatically renew it every two months with no further intervention from you. The wiki page has instructions for setting this up.
I'm afraid I'm not familiar enough with the cacert process to be much help. From what I can see on that wiki page, it sounds like your certificate should cover domain.com and *.domain.com, but I could be misreading that. If I'm reading that correctly, the name mismatch wouldn't be an issue.