Why do fresnel reflectors seem to be so hard to find? Seems like they’d be a good option here.
Do you mean just the lens? There's one in each of those old school overhead transparency projectors. Those should be easy to find. https://www.bhphotovideo.com/c/product/592006-REG/Dry_Lam_50...
A Frensel reflector doesn't led light through bit instead reflects the light. Basically the same idea as the parabolic dish, but as a flat sheet.