Chrome seems to have picked up my proxy settings no problem, I can go ahead and browse the web.
However, I can't "sign-in" to Chrome to pickup my bookmarks, apps, extensions, cloud printing, etc.
Any idea how to accomplish this?
I think the issue is that when Chrome signs in to the Google servers it uses a non-standard port to do so. It tends to be that most proxies will only relay a very specific range of requests on a limited number of ports (80, 443, 8080) and anything that falls outside of these will simply fail.
That being said however I am behind a corporate proxy and I am able to sign into Chrome absolutely fine, so it could be something else such as your proxy is filtering requests to Google's servers or the DNS lookup is failing for some reason.