What we do for commercial jobs is have the GC provide 6" wide heavy gage (gauge David) coil stock wherever we need in wall blocking. This is screwed directly to the face of the stud.. You could also use horizontal steel studs bay making screw tabs on the ends.
Personally I like 2 X 6's. If your studs are 16" on center cut the 2X material to 15 7/8"(ish) and notch (dado) the face of one end to clear the break (wrap) in the steel studs. Working from the notched end face screw the 2X in place through the stud and into the face of the 2X. Screw the other end through the stud and into the end of the 2X.
It's as easy as eating pie.
UA100