Wmi ManagedComputer SetServiceAccount gives “Set s

I'm trying to automate the post-install configuration of an SQL+SSRS server installation (MS SQL 2012 Express) -- I think it's more or less this. However, this is my first foray into Powershell, and I have never before configured or even used MS SQL. My server is a Windows 2008 R2 virtual machine, where I'm an admin, and the SQL server is installed locally (not clustered). I'm using Powershell v2.0 to run the following snippet (as an admin):

Write-Output("- Setting service account ...")
Write-Output("  - Loading assembly ...")
[System.Reflection.Assembly]::LoadWithPartialName("Microsoft.SqlServer.SqlWmiManagement") | out-null
Write-Output("  - Loading server ...")
$mc = New-Object -TypeName Microsoft.SqlServer.Management.Smo.Wmi.ManagedComputer "$hostname"
Write-Output("  - Loading service ...")
#$service = $mc.Services | Where {$_.Name -eq "MSSQL`$$sqlInstanceName"}
$service = $mc.Services | Where {$_.Name -eq "ReportServer`$$sqlInstanceName"}
Write-Output("  - Changing service account credentials ...")
$service.SetServiceAccount("$hostname\sa", "$sapwd")
Write-Output("  - Commit ...")
$service.Alter()
Write-Output("- OK.")

Between "Changing service account credentials" and "Commit", my code fails with this message:

Exception calling "SetServiceAccount" with "2" argument(s):
"Set service account failed."

The $sapwd is the password given during the SQL server installation. I'm never asked for a corresponding user name, but am told that there is an "SA" user is implied. I don't have a Windows user by that name on the local machine; I'm unsure of what users are defined in a (newly-installed) SQL server.

My goal here is the equivalent of using the GUI to set the "Service Account" to "Use built-in account: Network Service", The code snippet is based on this code. This post is not totally unrelated, but (a) it's not answered, and (b) I don't use clustering.

Many others have had this problem, but there don't seem to be any solid answers that work for me. How can I even find information about what this error means, and how to work around it?

Bonus

I'll also need to change the "Web Service URL" and the "Report Manager URL"; if you've any tips on how to do that you'll save me a bunch of hours.

sa is a database user (the builtin database administrator account), not a Windows user. For running a service you need a Windows user account. Usually either a dedicated account you created for running the service (with the required permissions/privileges) or one of the builtin default accounts like NT AUTHORITY\Network Service or NT AUTHORITY\Local Service.

Pass an empty string as the second parameter when using one of the builtin accounts, since they don't have a password:

$service.SetServiceAccount('NT AUTHORITY\Network Service', '')

With that said, normally you should have specified the runas account for the database service during the installation, so there shouldn't be a need for changing it afterwards.