DNS challenge is easy to pass and automate if you can programmatically add txt records to your DNS zone. Every major cloud provider supports this with command line tools, so it's a matter of moving the DNS zone there and writing a shell script and a cron item in the worst case.
I had a chance to skim through the link you posted - they are doing the http challenge verification (in step 6) for some reason which involves forwarding their domain into their internal network.
The DNS methods we already mentioned does not involve any of that - just a simple zone file change or a few clicks in a web UI to add a new record.