got it to work natively using invoke-webrequest. powershell guru here at work helped me out. Switched to the New Relic API version 2 (available at https://rpm.newrelic.com/api/explore), which uses JSON instead of xml, and made some sytax tweaks.
$json = @"{"alert_policy":[{"enabled":"true"}]"@
$headers = @{}
$headers["X-Api-Key"] = "j65k423lj4k2l3fds"
Invoke-WebRequest -Uri "https://some/working/file.json" -Body $json -ContentType "application/json" -Headers $headers -Method Post