I think you have a good chance, especially with the REU at cornell. If the prof you worked with likes you and wants you in his group, you are in. Otherwise, your stats say, "I'm a hard worker with a strong research background." That is certainly not bad and I think you will be a competetive applicant there.
Of course, being a "genius" AND having the above qualities is the best of both worlds for the applications panel, but if they had to choose between a student who scored 960 on the physics gre (or even 860) but had B average grades and no research experience, or a student who scores, say, 670 on the physcs gre but has perfect grades and excellent research experience, I would almost guarantee you they would go with the 670 gre.
A lazy and unmotivated genius only sometimes succeeds, but a hard-working and motivated bright person usually succeeds. This means that the abilities that you've shown you possess are more important to success than killing the GRE, and I have to believe graduate schools understand this.
The perfect apps are out there, but the majority of them have a weak spot here and there, and if you had to have a weakspot somewhere, I'd personally rather score 50-60th percentile on the gre than have bad grades or no research experience.