I was able to use the script to modify Word custom properties found here: 

http://blogs.technet.com/b/heyscriptingguy/archive/2010/04/06/hey-scripting-guy-how-can-i-add-custom-properties-to-a-microsoft-word-document.aspx

I modified the script so that I could feed it a CSV file for multiple properties--it works great! (THANK YOU!)

Modified Script:

#Set the PATH variable to the location where you saved the script and CSV file
$path = "c:\temp\PowerShell Scripts\"

#Set the DOC variable to the location of the document you want to update
$doc = "c:\temp\test.docx"
$application = New-Object -ComObject word.application
$application.Visible = $false
$document = $application.documents.open($doc)
$binding = "System.Reflection.BindingFlags" -as [type]

$customProperties = $document.CustomDocumentProperties
$typeCustomProperties = $customProperties.GetType()

$CustomPropertiesWorklist = Import-Csv $path\args.csv
if($CustomPropertiesWorklist.Count){
for($i = 0; $i -lt $CustomPropertiesWorklist.Count; $i++)
	{
	$CustomProperty = $CustomPropertiesWorklist[$i].CP
	$msoPropertyType = $CustomPropertiesWorklist[$i].Type
	$Value = $CustomPropertiesWorklist[$i].Value
	
[array]$arrayArgs = $CustomProperty,$false,$msoPropertyType,$Value

Try
 {
  $typeCustomProperties.InvokeMember(`
    "add", $binding::InvokeMethod,$null,$customProperties,$arrayArgs) |
    out-null
 }
Catch [system.exception]
 {
  $propertyObject = $typeCustomProperties.InvokeMember(`
    "Item", $binding::GetProperty,$null,$customProperties,$CustomProperty)
  $typeCustomProperties.InvokeMember(`
    "Delete", $binding::InvokeMethod,$null,$propertyObject,$null)
  $typeCustomProperties.InvokeMember(`
    "add", $binding::InvokeMethod,$null,$customProperties,$arrayArgs) |
    Out-Null
 }
 }
 }
 else
 
 {
	$CustomProperty = $CustomPropertiesWorklist.CP
	$msoPropertyType = $CustomPropertiesWorklist.Type
	$Value = $CustomPropertiesWorklist.Value
	
[array]$arrayArgs = $CustomProperty,$false,$msoPropertyType,$Value

Try
 {
  $typeCustomProperties.InvokeMember(`
    "add", $binding::InvokeMethod,$null,$customProperties,$arrayArgs) |
    out-null
 }
Catch [system.exception]
 {
  $propertyObject = $typeCustomProperties.InvokeMember(`
    "Item", $binding::GetProperty,$null,$customProperties,$CustomProperty)
  $typeCustomProperties.InvokeMember(`
    "Delete", $binding::InvokeMethod,$null,$propertyObject,$null)
  $typeCustomProperties.InvokeMember(`
    "add", $binding::InvokeMethod,$null,$customProperties,$arrayArgs) |
    Out-Null
 }
 }
 
 
 
$document.Saved = $false
$document.save()
$application.quit()
$application = $null
[gc]::collect()
[gc]::WaitForPendingFinalizers()

What I need now, however, is a way to REMOVE custom properties from a Word document (preferably using the same script).

Any ideas? 

Have you tried looking it up in the documentation?

Like this:
$typeCustomProperties.InvokeMember( "Delete", $binding::InvokeMethod,$null,$propertyObject,$null)
 

Sorry, I'm a PS newb... please bear with me...

That snippet is already in the script under the exception catch... It's used specifically to overwrite an existing property (per the link above). 

Catch [system.exception]
 {
  $propertyObject = $typeCustomProperties.InvokeMember(`
    "Item", $binding::GetProperty,$null,$customProperties,$CustomProperty)
  $typeCustomProperties.InvokeMember(`
    "Delete", $binding::InvokeMethod,$null,$propertyObject,$null)
  $typeCustomProperties.InvokeMember(`
    "add", $binding::InvokeMethod,$null,$customProperties,$arrayArgs) |
    Out-Null
 }

How then do I incorporate this method when I want to fully delete a custom property? Perhaps when one of these is true?

A. The value is blank for a specific property, delete the property

or

B. Add another column (called 'DelCP') where '1' to keep and '0' to delete

Any nudge in the right direction would be helpful and greatly appreciated. 

Thanks!

Just get it an delete it:

$propertyObject = $typeCustomProperties.InvokeMember('Item', $binding::GetProperty,$null,$customProperties,'CustomNumber2')
$typeCustomProperties.InvokeMember('Delete', $binding::InvokeMethod,$null,$propertyObject,$null)