Me. I use shared hosting on a server that runs a reverse nginx proxy to my nginx server. I don't have root on the server. I have a LE cert that I need to manually fiddle with DNS settings every 3 months to get. If you know how to automate it I'd love to hear about it.
Why doesn't their nginx proxy /.well-known/ requests for your domain to your nginx? Then you could just use `certbot certonly --webroot --webroot-path /path/to/webroot/for/your/domain -d your.domain.name -d www.your.domain.name` once and put `certbot renew` and nginx reload in crontab weekly, and you're good to go.
If you can't use HTTP-01 and must use DNS-01 challenge, I would check whether the software that runs your host's DNS management panel has an API in addition to manual mode. If not, I would check for ability to automate HTTP requests to that tool (parse the HTML, submit the forms, basically). My hope would be that the tool is popular and someone already did the work and code exists to operate it as if it had an API.
If you can do that, you can write (or find one already written) a certbot plugin that performs the DNS challenge using your credentials to the host provided DNS settings. certbot has number of plugins for the big hosting providers: https://github.com/certbot/certbot
certbot is the most popular Let's Encrypt client, but it's not the only one. Maybe another client has support for your situation. I would maybe ask the support of your hosting provider, maybe they know something.
