Add nested XML element

I'm trying to add a new RunSynchronousCommand element to the unattend.xml code below, but getting a bit stuck as it's nested a couple of levels in.

So far I have tried approaches such as this (amongst many others!), but banging my head against the desk now, so help appreciated.

$new = $doc.unattend.settings.component.RunSynchronous.RunSynchronousCommand[0].Clone()
$new.action = 'add'
$new.order = 3
$new.Path = "C:\ProgramData\Amazon\EC2-Windows\Launch\Sysprep\my_powershell_file.ps1"
$doc.unattend.InsertAfter($new, $doc.unattend.settings.component.RunSynchronous.RunSynchronousCommand[1])

This one gives the error:

Exception calling "InsertAfter" with "2" argument(s): "The reference node is not a child of this node."

This is the unattend.xml:

<?xml version="1.0" encoding="utf-8"?>
<unattend xmlns="urn:schemas-microsoft-com:unattend">
    <settings pass="generalize">
        <component name="Microsoft-Windows-PnpSysprep" processorArchitecture="amd64" publicKeyToken="31bf3856ad364e35" language="neutral" versionScope="nonSxS" xmlns:wcm="http://schemas.microsoft.com/WMIConfig/2002/State" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
            <DoNotCleanUpNonPresentDevices>true</DoNotCleanUpNonPresentDevices>
            <PersistAllDeviceInstalls>true</PersistAllDeviceInstalls>
        </component>
    </settings>
    <settings pass="specialize">
        <component name="Microsoft-Windows-Shell-Setup" processorArchitecture="amd64" publicKeyToken="31bf3856ad364e35" language="neutral" versionScope="nonSxS" xmlns:wcm="http://schemas.microsoft.com/WMIConfig/2002/State" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
            <ComputerName>*</ComputerName>
            <CopyProfile>true</CopyProfile>
            <RegisteredOrganization>Amazon</RegisteredOrganization>
            <TimeZone>UTC</TimeZone>
        </component>
        <component name="Microsoft-Windows-Deployment" processorArchitecture="amd64" publicKeyToken="31bf3856ad364e35" language="neutral" versionScope="nonSxS" xmlns:wcm="http://schemas.microsoft.com/WMIConfig/2002/State" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
            <RunSynchronous>
                <RunSynchronousCommand wcm:action="add">
                    <Order>1</Order>
                    <Path>net user Administrator /ACTIVE:NO /LOGONPASSWORDCHG:NO /EXPIRES:NEVER /PASSWORDREQ:NO</Path>
                </RunSynchronousCommand>
                <RunSynchronousCommand wcm:action="add">
                    <Order>2</Order>
                    <Path>"C:\ProgramData\Amazon\EC2-Windows\Launch\Sysprep\SysprepSpecialize.cmd"</Path>
                </RunSynchronousCommand>
            </RunSynchronous>
        </component>
    </settings>
</unattend>

I'm trying to add this:

<RunSynchronousCommand wcm:action="add">
  <Order>3</Order>
  <Path>"C:\ProgramData\Amazon\EC2-Windows\Launch\Sysprep\my_powershell_file.ps1"</Path>
</RunSynchronousCommand>