"Less expensive plywood...with knots in it" works just fine. Even rough hewn 1" X 6" plank subflooring works. However...the moisture content of the subflooring and the finished hardwood must be no more than about 4 percentage points of each other prior to starting the hardwood install. These moisture values are read by moisture meters. Since most DIY'ers don't have moisture meters in their tool arsenals, this is where simple common sense comes into play. IF the plywood (whatever the species) feels damp to the touch or has been stored outside by the lumberyard or the big box retailer, chances are that its moisture content is high. I've seen plywood at some HD stores that looked like it was hosed down before set on the sales rack. Buy the sheathing that seems driest. Stagger the end seams of the plywood. Fit them net to each other or just leave a 1/16" gap. In climates where the seasonal hunmidity swing may be high, gap closer to 1/8". Common sense is a wonderful thing.

I am a DIYer, so any pro responses could override my thoughts. 1/32" is nothing, IMHO. I installed engineered flooring several years ago over vinyl tiles glued onto concrete. The tiles were thin, but likely thicker than 1/32". Some of the tiles were loose, and I removed them. I did nothing to even the floor where the tiles were removed, because, as I recall, the installation instructions allowed me to ignore such minimal variations. The composition of engineered or hardwood flooring allow it to bridge over these. Also, because your unevenness is near walls, there will be minimal repetitive forces applied there. You could be double safe by applying a mortar-like product made to feather such variations. To me, this is easier and less messy than feathering by sanding.

You know, it's funny, but this very exact same discussion in going on between pros in the Pros forum over at John Bridge's website!! It has nothing to do with the weight of the stone. It has to do with a principle called "deflection". With ceramic tile, or most other floors, for that matter, the floor has to have a deflection of no more than L/360. Now, let me give you a real quick explanation of that figure. It's basically the unsupported length of the joists (in inches) divided by 360, and the center of the span put under a concentrated 300 pound load. For example, a floor 13 feet wide, in inches would be 156", divided by 360, would equal .43 inches (just under 1/2"). Under a 300 pound concentrated, centered load, that would be the most the floor could bend, before the tile and grout started popping or cracking. Now, no one goes around with 300 pounds, a string line, and a calculator. There IS an equation to figure out, using constants from different species of lumber used in framing, what the deflection of a floor is. With natural stone, because of the fact that as hard as it is, there are weak points in any stone, known as fractures, or faults (in some stones, seen as veining), the floor, in order to safely install natural stone over it, MUST have a deflection standard that's DOUBLE what it is for any other flooring. That is, L/720. It has to be twice as stiff. Up until about 5-6 years ago, the standard was actually L/420, but there were too many failures using that as a standard, and the industry increased it to 720. Now, most tile guys who know anything about deflection (and those ALONE are few and far between) RARELY know that those same deflection standards also exist for the subfloor, spanning across the joists. The reason so few know about it is because with ceramic tile, it's a non-issue, because 3/4" engineered wood (plywood, OSB, Advantec, etc.) will meet L/360, based on 16" centers. It does NOT, however, meet L/720 deflection standards, and for that reason, you need the extra layer of plywood, BEFORE cement board or membrane (cement board has no structural value. it's there only as a bonding surface). Class dismissed. :-)

Usually the added weight of the SLC which has got to be thick to cover the in floor radient heat, is not recommended over 16" center joists and just ¾" plywood. It is not stout enough, and then your adding more weight with the thinset and tiles. Usually the area is 12" center joists or at least 1¼" of subfloor, or the joists are blocked from below. It doesn't sound as if your GC is educated in proper substrate requirements for natural stone, which are double that od clay ceramics. Sealing the surface only prior to setting is a very good idea, as a texture tile surface is impossible to clean, thinset or grout from. It should be sealed before setting, and then come time for grout, it is already sealed and ready to go for the grout to be easily cleaned and wiped down. It depends on the size of your grout joints as to whether to use sanded or unsanded. 1/8" and smaller is unsanded territory, and wider then that up to 1/2" is sanded grouts territory.