Should I apply EA or RD?

If your chancing percentiles at JHU and UChicago are less than <20%, you are taking a much bigger risk in getting rejected rather than deferred or accepted. Tulane seems like the safer bet between the 3 but you should also know that Tulane fills most of its class with Early applications and that's why it looks good on paper, with high yields and low acceptance rates. Personally I think Tulane is not in the same category as JHU and UChicago in academics and reputation. They have figured out an effective way just like NorthEastern to prop up their rankings through exploiting the ED/EA market.

You didn't ask me for this suggestion but I will offer it nonetheless, I would apply early to a different school that is in the 20%-35% range if I were you. I don't know what that means but maybe run the numbers on NYU, Boston College, Tufts, NotreDame, USC, some smaller schools like Williams, Amherst, Colgate, Hamilton, Swarthmore. I think all of those are better schools than Tulane.

Forgive me for overstepping if I have and good luck with your decision.

Best.

That is just one angle. Yes, there are quite a few complications involved in early action, but you are still competing against less people for more seats. In my opinion, there is still merit in applying early action. If you aren't accepted, they'll sometimes defer you to regular decision.