First, I admit that this answer might not be acceptable on a work computer, if you can't install other versions of Chrome.
The answer is to install Chrome Beta and/or Chrome Canary, if necessary, in addition to Chrome Stable. I just tested, and I was able to use and sync the same Google account with a profile in Chrome Beta while also having it sync in my already installed Chrome Stable.
For those wondering, this isn't for work, this is all for personal use.
If you want details of the why, since Chrome got rid of the option to present a prompt when closing a window that has multiple tabs open on it, this is how I can always keep a window to the far left of all other Chrome windows, with my GMail/Google Voice/Chat, and some other tabs, open on it.
I'll only use this profile for that, and for opening links given in email, when it's convenient.
When I accidentally close that window (without using a separate browser profile), I can right-click and re-open the closed window, but it then appears to the far right of my existing tabs. Through third-party tweaks, I can move the window, but each time Chrome is completely closed and re-opened, it becomes necessary to re-move that window. It's very annoying for my workflow. There is another group of multiple windows and tabs I want to keep together that I'll now install Chrome Canary for.
Not an optimal workaround, but the best idea I've had recently.
I do use Hyper-V virtual PC extensively, but I don't want to have to do that for this purpose.