Thanks all,
I'll put aside a purely XSLT resolution and move on to a scripting solution.
I appreciate all your advice and time,
Mark

My question: is it possible to open that target XML file with a
parameter (such as the number "635") and then pass that parameter on to
the XSL processing instruction in some manner that makes it available to
"render.xsl"? If I can pass this single parameter through to the XSLT
stylesheet, my problem is completely solved. (Since my website is
non-commercial, I can insist that it is only available to browsers that
can automatically process XSLT).

Or, as both you and Martin seem to imply, must I use a scripting
language to achieve my goal of passing a parameter to the XSLT stylesheet?

If you want to process query parameters in a URL you need more than XSLT
I think, you can do that stuff with any server-side language (like PHP)
or framework (like ASP.NET or JSP) so you would load e.g.
  http://example.com/applyxslt.php?sheet=sheet1.xsl&number=635
and your PHP script applyxslt.php would then read out those parameters
and run the transformation on the server, setting stylesheet parameters
as needed.

Martin Honnen --- MVP Data Platform Development
http://msmvps.com/blogs/martin_honnen/