In method 1 you can avoid that the script stops when the VC is in trouble by adding the -ErrorAction SilentlyContinue parameter on the Connect-VIServer.

You will have to test yourself if the connected worked or not, and depending on the result retrieve the data or not.

Something like this

$vcName = "MyVC" 

$vc = Connect-VIServer -Server $vcName -ErrorAction SilentlyContinue 
if($vc.IsConnected){
# Collect the date
}
else{
# Connection to VC failed, display error message
  Write-Error "Connection to $($vcName) failed !"
}

Method 2 can indeed take a considerable time in a larger environment.

Here you can optimise the speed by using the Get-View cmdlet and by using the Property parameter.

Like this

Get-View -ViewType HostSystem -Property "Name","VM" 

and limit the properties to only the ones you need in the script.

Method 4 would my personal choice, you run/schedule the inventory script from a single station and you use a PowerShell feature to "multi-thread".

But be aware that the Start-Job in combination with a PowerCLI script needs some specific coding in your script.