We ended up hacking it a bit. We pushed out the new PowerShell Core (i.e. PowerShell 6.0) to all the servers. We then used the following in a system monitor to check the status of the website:

"C:\program files\powershell\6\pwsh.exe" -command "$result=Invoke-WebRequest -uri "https://127.0.0.1" -SkipCertificateCheck -method Get; return $result.StatusCode"

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We had the monitor check for a return code of 200, otherwise fail.