Latex paint is designed to allow more moisture loss than what you want. Log sealer is specifically designed for the proper rate of moisture flow through the membrane. There's several products available but most of us use Anchorseal. I prefer Anchorseal II and you can call the company that makes it (UC Coatings) at 888-363-2628 and buy it, or they can tell you where you can get some locally. I suggest using ASII not the original formula.
Drying time depends on the environment. Most will tell you to allow one yer for every inch of thickness so in your case it will take 7 years to reach EMC which is the acronym for equilibrium moisture content i.e. the point where no more moisture loss can occur without forcing it out via a kiln.
I do not believe the 1 inch per year rule is very accurate but no matter, it is going to take years before your slab reaches EMC whether that be 5 years or 10 years depends on the species and the environment it is in. You don't have to wait that long before putting it in service necessarily depending on the joinery you use for the frame and the finish you choose but you will need to do a fair amount of research.