Can I specify custom DNS records on your end so I can test our staging environment while leaving my current site live on my old server?

No, we don't have a way for you to supply custom DNS records.

However, we suggest two ways you could go to achieve this:
  1. Give it a name in DNS, e.g. staging.example.com and test against that
  2. Test against the IP address. If you have a virtual host configuration, you can add headers to the URLs and specify a "Host" header. This will tell your server that our load generators are accessing it via the hostname in the header, even though they are really using the IP.