In order to solve this problem, I upgraded the head node’s PowerShell to v2.0 (HPC Server ships with PowerShell 1.0) and was now able to use the Start-Process process. This leads to having the script run in no time at all. Here is the code:

#Uncomment line below if running from a regular PowerShell Window
#Add-PSSnapin "Microsoft.HPC"
#Change the HPC-HN value below to match the name of your head node
$HEAD_NODE = "HPC-HN"

#Obtain Compute Nodes
$nodes = Get-HpcNode -GroupName ComputeNodes

Write-Host "Setting Head Node To:" $HEAD_NODE
Set-Content Env:CCP_SCHEDULER $HEAD_NODE
#Stop Head Node Services
Stop-Service -Force HpcManagement
Stop-Service -Force HpcNodeManager
Stop-Service -Force HpcSdm

$services = "HpcManagement", "HpcNodeManager"
#Stop the services on all compute nodes
foreach ($node in $nodes)  {
foreach ($service in $services) {
 $serviceStop = "net stop $service"
 $computer = $node.NetBiosName
 $computer = "\\$computer"
 Write-Host ("Executing command: psexec " + $computer + " " + $serviceStop)
 Start-Process psexec -args ($computer + " " + $serviceStop)
 }
}

Write-Host("Waiting 10 seconds for services to stop")
#Change the value below if you have a large number of nodes
Sleep(10)

foreach ($node in $nodes)  {
foreach ($service in $services) {
 $serviceStart = "net start $service"
 $computer = $node.NetBiosName
 $computer = "\\$computer"
 Write-Host ("Executing command: psexec " + $computer + " " + $serviceStart)
 Start-Process psexec -args ($computer + " " + $serviceStart)
 }
}
Write-Host("Waiting 20 seconds for services to start")
#Change the value below if you have a large number of nodes
Sleep(20)
#Start Services on Head Node
Start-Service HpcManagement
Start-Service HpcNodeManager
Start-Service HpcSdm
Write-Host("Your nodes should show up in the heat map in a about a minute")

And of course, we need to have a video. Here is the script in action with 4 nodes that are not displaying their info on the heat map: