Aha - now we have something to go on - let's dig into your situation.
As a reapplicant, EssaySnark *always* recommends reapplying in Round 1. This shows commitment/enthusiasm - in fact, a few schools even require reapps to come in the first round. We'd go with the advice you got from the adcom about this.
For the schools that you are applying to "fresh" - it might make sense (this is a big "might") to hold one back for Round 2. The only reason to do this would be if you don't make progress with the Round 1 apps - if you haven't even been invited to interview, for example - then you know that something is still off with your strategy. You've probably already done a lot of course-correction since you didn't make it in last year, so hopefully you've accounted for whatever wasn't working before. But, as a safety measure, you might want to hang onto one of your top-choice schools to target in Round 2, and then use those Round 1 apps as your guinea pigs. For many Round 1 schools, you'll know by late November if you're in the running (interview invites) and for some you'll get a final answer in mid-December, which would be enough time to pull together a Round 2 app if you needed.
So, we're also leaning towards Round 1 for you, for the same reasons that you were thinking of. You could possibly hold one of them back just for this strategic issue. You wouldn't do so based on your profile alone.
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