Some universities are excellent for both chemical engineering and math. MIT and Stanford come to mind. Some schools are excellent for math, but not for Chem E. Harvard comes to mind, but I am pretty sure that Williams College also fits this description.
You should go through your list and make sure that each school is good for both of your possible majors.
The other issue that comes up is budget. You might want to run the NPCs for a few schools and see what the results look like. I would be skeptical about how many out of state public schools will fit with “Will probably need most if not all costs covered”.
Otherwise you are doing very well. Congratulations on your accomplishments up to now.
I went the Chem E route at UH as a NMF. Full ride and great Honors College so a solid safety.
Note that ChemE specialties vary by school. Purdue is strong in engineering for consumer products as well as chemical manufacturing.
UH, A&M are going to be more oil driven. Some more chemicals, paints, polymers. Ivies will often lead to consulting. I know a couple Chem Es from Notre Dame who made it up to VP in Finance at Fortune 50 CPG. Another friend was a Purdue ChemE who started at the same Fortune 50 as an R&D Engineer. He got a top 50 MBA and transitioned to finance at the same company. He’s now CFO of an oil company.