It is possible to add IP addresses or IP address ranges to the whitelist for your staging environment so that requests from those IP addresses will not require the basic authentication. It sounds like that might be the easiest path for you at this point. In order to get that setup, I'd suggest submitting a request via our Customer Case Portal (the "Support" tab up above). Our support team should be able to assist with adding the necessary IP addresses to the whitelist. You will need to provide them with the externally-facing IP address that the requests will be coming from.