Yes, both Tuck and Columbia have early decision. This will slightly increase your chances of getting in, but then you will have to withdraw your other apps if admitted. Kellogg interviews everyone. You can initiate interviews at Duke, Tepper, Georgetown and a few others before a certain date (mid October usually).
I used a similar strategy which worked out for me, but with a lower set of schools since I had lower test scores. I applied to schools ranked 15, 19, 22, 28, 29, 33, 44 (all of which I considered reach schools with my 660 GMAT + 1.5 years W/E), and was actually only dinged from #44. I then reached for 2 more schools in round 2, but I knew that I probably maxed out in round 1 so I didn't push it.
It's a lot less stressful to be admitted in Round 1 which is why a lot of people apply to 2-3 targets and then 3-4 reaches. You might also learn something from your earlier applications and be able to write stronger essays for your round 2 apps, in which case it would make sense to save a few top choices for round 2. But then again, if you apply to your top 6-7 in round 1 and get in, then you are done... good luck.