What I told you was that I had declined the offer of a raise and promotion at my current job in favor of the Institute. What I didn't tell you was that I had then called the Institute and asked them to raise their offer.
This—declining offer A and then pushing back on offer B—is dumb. Don't do this. It turned out OK for me, but it would have been safer and probably more lucrative to hold my options open and give less information to my opponents1. The reason I didn't: I have a certain amount of cowardice that I have historically only been able to overcome by a somewhat forced overconfidence. It isn't pretty.
Anyway, after letting me sweat over the weekend, they offered a small salary bump and I accepted. Is a month and a half's rent per year for the rest of my working life worth three days of stress? Well, when you put it that way, of course it is. But it was pretty stressful and I had to exercise a certain amount of rationality to convince myself to do it. (This was, in fact, the first time I have ever asked for more money from any employer, not counting the time I told that part-time dude that I wanted to quit and go back to part-time but couldn't unless he raised my rate.)
I start the new job a week from today. Although I will admit to not having searched as widely as I could, it seems to be a Pareto optimum among realizable jobs for me at this stage. I can imagine Tufts jobs that would beat it, but my applications for Medford-campus jobs did not generate responses—I suspect because they're a Solaris shop and I don't have a solid Solaris bullet on my resume.
What's going to be hard is asking again next year. It's hard to calibrate expectations, since I don't have access to the salary database and local geek society tends to keep salaries confidential.
1Doesn't it suck that, before you get to cooperate like both parties want to, you have to play a zero-sum game for stakes that are way higher for you than for them?