You should also have a 6 mil poly film barrier on the slab and on top of the screeds. Even though you have proven that there is no moisture in the concrete, humid summer time air will condense on the cool cement, and form water droplets. This should be minimized with this double layer of poly. And for extra insurance you should be using pressure treated 2 by 4 ‘s and kiln dried (to 6%-10% MC depending on your area) so they don’t warp out of place. Don’t install any screed boards over 4 feet, also make sure to overlap and randomize the rows, so you have a more random nailing surface. To assist the glue you can use powder actuated nails, Tapcon screws, or expanding concrete anchored screws. This will be just to hold down the ends of the wood until the glue dries under the screeds. In this type of floor the joints that fall between the screeds will be weak points in the floor. Years later, you may get the occasional broken board between the screeds as the floor gets sanded thinner, but this is fairly simple to repair.
And that brings me to the next method, as we go down the choices, fastening a plywood subfloor directly to the concrete. The methods suggested so far keep the wood and concrete more or less separate, and allow for the different rates of expansion of these dissimilar materials. When you try nailing wood, even plywood directly to the slab, you’ve got to take care. Don’t try to nail down one thick layer of plywood, this rarely works in the long run. And the 3/4″ plywood most commonly available is not thick enough for the 2″ flooring nails (never use staples) to penetrate the required 7/8″. It is too stiff to follow any minor undulations in the concrete and will put undue stress on the fasteners. Instead install 2 layers of 1/2″ plywood in opposing directions. You should lay a heavy poly film down first, with the seams taped. Then install cork or foam pad on top of that to protect this moisture barrier from getting punctured by the plywood. Float the first layer of plywood in one direction. Then glue and screw (with short 3/4″ screws) the next plywood layer (in the opposite direction) so that no concrete is damaged. This is the best system for installing on a heated slab system. Can’t use nails in the concrete here.
But if you insist, you can nail the first layer of plywood with powder actuated nails. These powder driven nails are tricky to use and you must test the concrete for suitability.