What are his math teachers saying? Do they think he should be in Pre Calc? It’s natural for a Senior to be in pre-calc and of course, many we see have it junior year and take Calc.
Unless his teachers say he’s not ready, I would stick with pre-calc and then stats next year.
While the schools you note aren’t overly competitive admission wise (Colorado could put him in exploratory, I suppose), Mizzou says this below - and if i’m reading for management (not the most quant heavy major), they require math 1400 - which is Calculus - so wouldn’t you want to be exposed now?
Maybe if he drops down, I’d still take pre-calc but maybe senior year.
But ultimately, I’d listen to the teacher from last year - where do they think your student should be?