I totally believe that you can get significant percentage improvements with the right mix of particle sizes, but the LWIR emittance of just about all nonmetals was upwards of 75% the emittance of an ideal blackbody. That puts a ceiling of about ⅓ (4:3) on the possible improvement on that end. And plain old whitewash has a reflectivity upwards of 90% in the visible, while the best known materials, such as polished silver, are something like 96%, so you might get 3:2 on that end—but probably won't even get 2:1. https://nvlpubs.nist.gov/nistpubs/bulletin/07/nbsbulletinv7n... is one older reference on this, but https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=90... gives plots of silver mirrors' reflectance by wavelength, polarization, and angle of incidence.
As a side note, what people have been painting their houses with for thousands of years isn't normal milled limestone; it's slaked lime, which forms limestone by absorbing CO₂ from the air over about a month. Modern whitewash has milled limestone mixed into it, but the morphology of the final surface isn't very similar to milled limestone in a transparent binder.
That effect is almost not perceptible in normal milled limestone.