Hi littlestone,
As imSKR pointed out, the GRE places a greater emphasis on your vocabulary knowledge (and when to use certain words instead of others), so your capacity to score 160+ on the GRE Verbal would likely come down to how quickly you could improve your vocabulary knowledge. With a 650 on the Official GMAT, you are closer to a 680+ than you probably realize - and since you have put in some significant GMAT Study already, you would probably be better served by sticking with the GMAT at this point (although you could potentially take both Tests if you wanted to).
Before I can offer you any additional advice for your studies, it would help if you could provide a bit more information on how you've been studying and your goals:
Studies:
1) When did you take your 2 Official GMATs and what were your Quant and Verbal Scaled Scores for EACH?
2) How long have you studied in total? How many hours do you typically study each week?
3) What study materials have you used so far?
4) On what dates did you take EACH of your CATs/mocks and how did you score on EACH (including the Quant and Verbal Scaled Scores for EACH)?
Goals:
5) When are you planning to take the GMAT? For your next attempt, are you planning to take the At-home GMAT or are you planning to take your GMAT at a Test Facility?
6) What specific application deadlines are you facing?
GMAT assassins aren't born, they're made,
Rich