What a nightmare. I'm sure there are use cases for a setup like this, but this is not the system I'd like to maintain. I use Jekyll because of it's simplicity. I edit my site in my favorite text editor and rsync to shared hosting.
I use hugo and then setup my output folder (where the generated output goes) as a git repo. Generate the site -> git commit/push -> Caddy. Caddy has a feature to pull in content from a git repo so when you couple that with the built-in Let's Encrypt support it makes it dead simple.
I stopped using Caddy when I discovered that it didn't support one of the unusual TLDs I had. Maybe I should give it another go, though. That was over a year ago.
I assumed it was because of the TLD, because everything else was otherwise identical to some of the other virtualhosts.
It was a bit of work to get everything running, but there's very little to actually maintain afterward. I'm definitely going to start replicating the setup elsewhere (including my own homepage, which is currently down due to its VPS having failed hard and me not having enough time to rebuild it).