So College Transitions has scraped some basic merit information out of the Common Data Set reports of various colleges. When getting serious about applying you need to go to their actual websites and such, but this is a good resource for a quick overview:
The basic issue is while all the Reach colleges you identified do have merit programs, only a small percentage of students actually get much merit (independent of need).
Of course if you are OK likely just attending one of your in-state options–that’s perfectly fine. But there are some other options.
Minnesota is a strong Biochem school which has a pretty low OOS COA to begin with, and then also offers OOS merit which they will include in their NPC output. It could be interesting just to have it as an alternative, even if you end up choosing a Texas public instead:
Case Western is then a private with very strong Biochem and actually a much higher percentage of students getting significant merit offers. They may want to see some serious demonstrated interest, but it could be worth doing that, again to get at least another interesting alternative to your in-state publics. Their program is interesting in part because it is actually hosted out of their highly-regarded medical school:
And then Rochester is another I would put in a broadly similar category to Case in terms of being a private that is strong in Biochem (again co-hosted out of their med school) with a robust merit program, although in some ways it actually might be the closest in overall curriculum structure and vibe to some of your current colleges like Rice and WashU. Technically Biochem there is a track within Bio but I think the content ends up similar anyway, and there is definitely a lot of relevant research (particularly for an institution its size):