About multi-server operations

Thank you for your help.
Currently, I set my own domain as a rental server and some subdomains as VPS.
I'm thinking of moving the rental server this time, but I'm having some trouble.
VPS uses DNS authentication in certbot for automatic certificate renewal, but you must add a record called __acme-challenge と in the API.
The DNS attached to the rental server I am currently using can be operated by API, but the DNS attached to the rental server I am migrating to cannot be operated by API.
I was thinking that I should send A record to the destination server on the server I am currently using, but according to the documentation of the destination server, I have to change the name server if I want to set up a free Let's Encrypt certificate.
By the way, I tried SSL setting with A record pointing to the destination server, but I still couldn't set it because I got an error saying, "The name server is not the name server specified by this service."
Also, I thought about specifying the name server of both the source rental server and the destination rental server, so I tried it in a domain that I didn't use, but it didn't work.
Also, certbot on the VPS issues wildcard certificates, so you cannot authenticate with http.
Also, adding the __acme.challenge を record manually is difficult because you want to automatically renew the certificate.
I think there is not enough information, but is there any other way?
Thank you for your cooperation.