First, thank you for engaging on this thread. Its nice to see a student so thoughtful in your approach and responding to everyone.
I can understand your need for merit aid, and you’ll hear of lots of schools that offer this, even though it may be rare to actually get aid from them. When my first daughter was applying, we sort of “heard” who offered aid (e.g. through this forum, from the school literature, etc), and applied to those schools and mostly struck out on aid except at some schools well below her stats, but she got lots of acceptances. She ended up at Cornell, I didn’t get any financial help there, they don’t offer academic scholarships, and so I (gulp) paid full fare.
We got smarter for my 2nd daughter, and had a better hit rate for merit aid. Some background: some schools apply their aid as financial aid: the Ivy’s, many other top schools, etc… If you come from a low income family, you’ll get your best deal from these schools which also happen to be the top schools - they don’t have to offer merit aid to anyone because everyone wants to go there. “common knowledge” is wrong, very low income students can afford Harvard/Cornell/etc - it will be essentially free for them and cheaper than the local community college, the hard part is getting in!
If you have an upper middle class income, you’ll want to find a school thats “buying” good students with their aid. How do you find them? Look at the “common data set” for the school in question (google search: common data set ‘school name’ ). You’ll see lots of interesting numbers, but in section H it will say how much the school gives for financial aid, and how much it gives for academic scholarships. For instance, Tulane had 1909 full time freshman last year, 802 of them were awarded non-need based (ie. MERIT) aid, at an average of nearly $24K each. I challenge you to find a school that does better on this metric, and it’s an excellent school too!
Anyway, looking at the common data sets, you’ll find that a lot of schools which talk up their merit aid, don’t really offer it much. “Deep pockets and short arms” as a friend of mine says. So don’t bother applying there if you are targeting getting merit aid.
OK, so with a 33 ACT for Tulane, you may get in, but aid might be more of a trickle than a stream. Take that ACT a few more times till you hit a 34-35, and you should have a better shot at aid there and elsewhere, and the aid will make the fees and time you spent on the ACTs look well invested, and this will apply to other schools as well. Try the SATs too, you may do better on them.
I don’t know your other stats, so your mileage may vary, all disclaimers apply 
. (my 2nd daughter took the SATs, then the ACTs 3 times: 34, 34, 36, bingo! again, your mileage may vary, what helped her know she could do better was that the sub scores varied on the first 2 runs, so she knew if she could hit her best in all categories on the same day it would be good, and she was trying to tie a friend’s 35. She got a great aid package at Tulane, but frankly she liked the school so much she would have gone there anyway).
Anyway, as you search for “aid”, look at the common data sets and target the schools that have historically given aid.
Best,
Ken