New-WebServiceProxy : The HTML document does not contain Web service discovery information.
At C:\myScript.ps1:91 char:17
+ ...    $Service = New-WebServiceProxy -UseDefaultCredential -uri $webServ
+                   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : InvalidOperation: (http://mySharePoint....bin/Search.asmx:Uri) [New-WebServiceProxy], InvalidOperationException
    + FullyQualifiedErrorId : InvalidOperationException,Microsoft.PowerShell.Commands.NewWebServiceProxy

First attempt at calling the search.asmx service.

$webServ = "http://mySharePointsite.com/_vti_bin/Search.asmx"
$Service = New-WebServiceProxy -UseDefaultCredential -uri $webServ
[xml]$Results = $Service.Query($QueryPacket.OuterXml)

After adding ?wsdl to the uri string, it worked.

$webServ = "http://mySharePointsite.com/_vti_bin/Search.asmx?wsdl"
$Service = New-WebServiceProxy -UseDefaultCredential -uri $webServ
[xml]$Results = $Service.Query($QueryPacket.OuterXml)