Update: I was not able to directly do what I mentioned but we found a workaround for anyone in future with a similar issue. Powershell can do invoke-Webrequest and can do windows authentication via -UseDefaultCredentials.
You can’t use powershell directly, however you can use python. So, we used the python integration extension and the python subprocess module to invoke these requests in a loop to download the files we needed. Then, in the same script we setup the flow variables required to give the workflow access to the files. This works really well and is far simpler than what I was originally attempting