The sad thing is: There would be an easy solution to solve this trickery. Just giving Firefox a right click option. Not "open in new window", not "open in new tab" but "open in clean (aka cookie free) window".
With I had the coding skills to realize that. Or is there already something similar out?
Mozilla's BrowserID focused more on a really good way of managing a single identity (per Firefox profile), whereas Chrome's MultiProfiles were focused on easily switching between multiple profiles with separate cookies, history, passwords, etc (whether that's for multiple people or a single person with multiple but separate needs online).
Multi-profiles seem good for your need...you can stay signed in with a persistent google cookie in one window (maybe just keeping gmail open), while doing all your regular surfing without the cookie in another window, under a different profile.
Both are still in development though. I don't see multi-profiles in about:flags in chrome, and some poking around shows you might need to run chrome with a command flag, which is a pain. Reviewers seem to like it, though.
edit: it's not a nice integrated browser function, but I guess you could get equivalent functionality by just running different Firefox instances with different profiles. I don't know if there are any problems with that approach, though.