There are several points to keep in mind.
First, the key to heating a bare floor is to make the temperature as even as possible, otherwise you will have noticable cool spots in the floor. You will probably have that somewhat anyway where the joists are, but you want to aleviate that as much as possible. Because of this, I wouldn't recommend the aluminum plates. They don't do that good of a job of distributing the heat, and the floor will be very noticably warmer directly above the pipes, and cooler the farther you away you get.
Because of this, you would be better off either looping pex pipe on the sides of the joists (NOT against the subfloor) and insulating below as much as possible. A good product to use is R-Board insulation with foil on the one side. Put the foil up to provide a radiant barrier and to reflect the infrared rays upwards to warm the subfloor. You can also use fin tube as suggested, and it will work just fine.
Second, you will probably need about 150-180 degree water to make the floor nice and warm on bare feet, so a mixing valve may not be required. Obviously, if you use pex, and your water gets to 220 you are exceeding the operational limits of the pipe, so the fin tube and copper pipe might be a better option.
The other thing is, does your boiler need to get that hot to heat your house? Most baseboard heating systems are sized to provide the required heat output using 180 water temps. Usually, outdoor reset controls are porgrammed to provide water temps between 140 and 190 degrees depending on how cold it is outside. If you can limit it to something under 200 degrees pex pipe would be the easiest and quickest to install, and could be used without a mixing valve of any sort.