Generally speaking, a popular way to solve problems like this is to centrally manage the certificates and then push or pull them to the servers.
For example, you might have a local machine handle all the challenges via DNS-01, then a script will upload them onto each server and reload the web server; or the servers might load the new cert daily from a local server. Some people even use a network mounted volume on each server to host the certificates, so there is one write and 1000 reads.
You can also centrally manage HTTP-01 authentication by using redirects or proxying all requests to /.well-known/acme-challenge on your system into a single server.
I wrote/maintain a system for scalable (domains or nodes) ACME deployments. It is a centralized certificate manager that creates a local API for your servers to request/deploy certificates through, either through a programmatic API or a custom openresty/nginx module : GitHub - aptise/peter_sslers: or how i stopped worrying and learned to love the ssl certificate