Hi Roy,
Looks like you have a lot of good answers to your question. Mine will follow along the same lines: yes, Round 2 is tougher than Round 1, but frankly, timing is just one of many quantifiables that go into a successful graduate application for business school. The most important thing is to put together your strongest possible application.
Assuming that Round 1 is your target, if you can take the GMAT earlier, do so. HBS, Wharton and Stanford are all posting September deadlines this year, so taking the test in September would be cutting it close -- particularly if you don't like your score and decide to take it again.
To help you assess this, I'd want to know more about your background, what you studied in undergrad, what kinds of GMAT prep you're using, how much of your study is review and how much is learning new material, and what you're scoring on timed practice tests. I would also want to know which top MBA programs you are targeting.
So, many points to strategize here, but the key takeaway is: we all agree that it's best to get a final GMAT score at least a month or two before the first deadline you're aiming for. Only you would know, taking into account all the points above, whether that makes Round 1 or Round 2 more realistic.
Hope this helps,
Margaret Strother