Can’t disagree with your take. If Tulane’s not affordable per the NPC or you want to compare offers and/or it’s not a clear first choice, then you can’t apply ED. Make sure to apply EA, which has a higher rate of acceptance (this year 10%) than RD (low single digit acceptance rate).
As long as you have a balanced list (2-3 reaches, a handful of matches, and at least one (ideally 2) affordable safeties), things will work out.