First of all, those are two separate suggestions. The first procedure is required to use the second.

"Using a document name (such as "516bb1eee3bc424aaa1b3e98bae5fb5b.doc") in my Normal template code would only work for that particular document and none of the others. "

Yes, but you can GET the name of any given document. or use ActiveDocument (the current one).
[vba]
Dim Doc As Document
Set Doc = Documents("516bb1eee3bc424aaa1b3e98bae5fb5b.doc")
Application.Run Macroname:="doc!ThisDocument.KillTheForm"
[/vba]

change it to:
[vba]
Dim Doc As Document
Set Doc = ActiveDocument
Application.Run Macroname:="doc!ThisDocument.KillTheForm"
[/vba]

However, you STILL have to have the procedure in that document.

"The first suggestion does not work for me because one of my constraints is that I can not add/edit any procedures to the individual Word documents. The Word documents are created by a document management system that is outside my control and there are hundreds of them being actively used and shared between many different users."

What is stopping you? You can do this once for a document, and the module stays put. Say you have 516bb1eee3bc424aaa1b3e98bae5fb5b.doc, and it is Active. It is thus ActiveDocument.

Previously (and again you only need to do this once), you write a standard module with its content being:
[vba]
Option Explicit

Sub KillTheForm()
Unload frmPointLinks
End Sub
[/vba]

You Export it as a .bas file. Right click it, and Export. You can save it anywhere, and name it anything. I saved it as c:\KillTheDamnForm.bas

Now, in Normal, you have the closing procedure ImportThenExecute:[vba]
Sub ImportThenExecute()
Dim Doc As Document
Set Doc = ActiveDocument
Doc.VBProject.VBComponents.Import "c:\KillTheDamnForm.bas"
Application.Run Macroname:="doc!KillTheDamnForm.KillTheForm"
End Sub
[/vba]

It:

1. imports the KillTheDamnForm module into ActiveDocument (currently 516bb1eee3bc424aaa1b3e98bae5fb5b.doc)

2. executes the procedure KillTheForm

and the userform is closed.

This STILL seems silly to me. I would add a boolean DOCVARIABLE to be able to test quickly if the code module has been previous imported. If so, then just execute the userform closing procedure.

You have constraints, true, but - for the Nth time - if you know EXACTLY what you want to do, it is possible some of that can be achieved.

Let me reiterate. Constraint #1

"I can not add/edit any procedures to the individual Word documents."

Why? Because you are not supposed to, or because you do not know how to do it?

Constraint #2

"because one of my contraints is that each Word document has it's own unique file name (project name)."

Not a problem. ALL files have unique names. VBA code is deisgned to function with them.

So....can you close the userform? Yes. Can you "mimic" what the user would do manually? I am not so sure.