Thanks Steve. Yes I have, although the changes do seem to take effect immediately. IOW, ProxyServerA works, change to ProxyServerB, ok out of Tools..., fails, reverse this, works, all without restarting SSMS.
I know this isn't a network configuration forum, and my IT department should figure this out eventually, but they'll have to escalate to a 3rd party external support organization, take weeks (or may just bail on the issue), etc. I was hoping to help them out a bit, and get my problem solved quicker via this forum.
I fully admit this isn't urgent - I can manually check for updates (i.e. Google), download the installer(s), and install manually.
Still, it would be interesting to know why this is failing...