I'll be honest with you. You're in a very similar situation to the one I was in last year. I had a 550 (20%) and a decent GPA and 3 different research groups I'd worked with (roughly about 2 years, so slightly less research than you). I ended up with 7 rejections from 7 applications. However, the one thing you really having going for you is that a Nobel Laureate is a reference for you (you also have a bit more research experience than I had at the time). If that were not the case, I'd recommend applying to schools that didn't require the PGRE and then trying to transfer after a year or two.
Honestly, if I were in your situation, I'd go ahead and apply to some of the upper tier schools you want to go to. However, I would also throw some applications out to ... erm ... "lesser known" programs. My profs last year told me it would probably be easier to go to a crummier program for a couple years and transfer out than try to get in to a good program with my PGRE at the time. I've basically reiterated what the last two people told you to do.
If you're wondering, the second time I took the PGRE I raised my score to a 710. Not fantastic, but a huge improvement nonetheless. Just because you did horribly the first time, it doesn't mean you're destined to do horribly the next time.