I feel that you have the mindset of a beginning graduate student in pure math, but who is trapped inside a graduating high school senior’s body, and who unfortunately isn’t accepted to “prestigious” math undergraduate programs. I have two additional comments about your situation, speaking as someone who teaches engineering at a large state school similar to WSU and doing theoretical research but is not a mathematician.
First, given your passion in abstract algebra it appears that WSU would be a better fit than Tulsa because WSU likely has three to five faculty members in each area of math who you could request to work with or take advanced classes from, something Tulsa is unlikely able to match. Furthermore, in case your interest in math changes from abstract algebra to a different area of math as you grow, WSU (or any large state school for that matter) would have the breadth in their faculty members to hopefully meet your need.
Second, while it may be disappointing to you to “settle” on WSU, there are numerous success stories of students making the jump from state schools ranked around 100 to schools that are peers to the 12 that waitlisted/rejected you. Last year alone my department has several graduates who are accepted to M.S./Ph.D. programs in engineering at UIUC, Georgia Tech, Virginia Tech and the likes. WSU isn’t going to be the reason they don’t take you. If you are able to produce some publishable results during your 3+ years at WSU, it would look outstanding in your grad school application. If you couldn’t, then perhaps a mathematical research career isn’t for you (and there is nothing with that).