Piping the powershell output to Write-Host was sufficient to get it to work for .xml files, but it broke on .gz files.
However, following the suggestion here: (https://github.com/JuliaPackaging/WinRPM.jl/pull/81), I changed the download function to a call to BinDeps.download_cmd, and that worked fine. BinDeps is also using the powershell DownloadString cmdlet for downloading, but it looks like they invoke a much more robust call than what I was trying.
