Well this was painful and embarassing. I figured out the root cause of the issue I was seeing with the timeout. I had set the timeouts to "defaults" that were 3 orders of magnitude smaller than the real defaults. So even when I increased them to what I thought were really large values, I was still shorter than the defaults.
I had skimmed through the wording on the Microsoft page describing the setTimouts() method and misinterpreted the timebase of the parameters. I assumed seconds while it was actually milliseconds.
During the process of debugging this issue, I duplicated the code using the alternative COM object, "WinHttp.WinHttpRequest.5.1", and in verifying the equivalent API, SetTimeouts(), discovered the faux pas.
I did learn a few things in the process, so all is not lost, "WinHttp.WinHttpRequest.5.1" has a SetAutoLogonPolicy() [3] method that allows me to skip the hokey "proxy" foolishness required with "Msxml2.ServerXMLHTTP.6.0" to force it to send the user's credentials to an intranet server. I also fiddled with Fiddler [4] and learned enough to be dangerous!
Hopefully someone else can learn from my mistake and find this useful in debugging their own issue in the future.
Here are some inline links since I don't have enough rep to post more than two:
[3] : msdn.microsoft.com/en-us/library/windows/desktop/aa384050%28v=vs.85%29.aspx
[4] : fiddler2.com