Powershell equivalent of 'openssl dgst -sha512 -sign' - powershell

Question

For API access, I need to sign a JSON file with 'openssl dgst -sha512 -sign'. I need to run this in a powershell script.
Currently, I am using the following method:
Write the file to a temp file, and re-read it to be certain that there is no conversion problem
Invoke openssl to sign the file
Read the signature file
Call the API
$body = #{
"login" = "customer"
"nonce" = Get-Random -Minimum ([int]([math]::pow(10,8))) -Maximum ([int]([math]::pow(10,9)-1))
"read_only" = "true"
"expiration_time" = "30 seconds"
"label" = "Test"
"global_key" = "true"
} | ConvertTo-Json
Remove-Item -Force "D:\temp\body.tmp" -ErrorAction Continue
Remove-Item -Force "D:\temp\body.dgst" -ErrorAction Continue
$body | Out-File -FilePath "D:\temp\body.tmp" -Encoding ascii
# Re-read data from the file after it's been re-encoded to ascii (as thats what we signed)
$body = [System.IO.File]::ReadAllBytes("D:\temp\body.tmp")
# Sign with the private key of the signing certificate
& D:\apps\openssl\bin\openssl.exe dgst -sha512 -sign "D:\powershell\TransIP\sign.txt" -out "D:\temp\body.dgst" "D:\temp\body.tmp"
$headers = #{
Signature = ([Convert]::ToBase64String([System.IO.File]::ReadAllBytes("D:\temp\body.dgst")))
"Content-Type" = "application/json"
}
I've been searching for a native Powershell/.NET method for SHA512 digest signing, but I can't seem to find anything in the Security class to do this.
Does anyone know a native Powershell method (thus eliminating the dependency of an external openssl installation), or is the above method the only method for signing?
Documentation of the API that I'm trying to use: https://api.transip.nl/rest/docs.html (section 'Authentication'). I've already asked TransIP for support, but they don't support Powershell.
Documentation of 'openssl dgst': https://www.openssl.org/docs/man1.1.1/man1/dgst.html
Joost