For the benefit of others, in the start-upgrade.ps1 I modified the logfile variable to:
$Logfile = "C:\ProgramData\Windows10RequiredUpgradeStart-Upgrade-$env:USERNAME.log"
In the wrapper.vbs I added strUserName to the first 'Dim', then
Set oWsh = WScript.Createobject("WScript.Shell")
strUserName = oWsh.ExpandEnvironmentStrings("%username%")
under strComputer
And just a bit further down where the path for the logfile is declared:
path="C:\ProgramData\Windows10RequiredUgradeWrapper" & strUserName & ".log"
Putting the logfile in the user profile would be a good approach too but I like having one place to check.
Thanks again for your great work.