If you have a table saw you could rip 2x4's in half and piut them
perpendicular to the length of the wall. That would probably have less
flexing than using 2x4's sideways. You could also buy 2x2's, but they
cost more that 2x4's. About 10years ago we had a big flood in certain
parts of town, and afterwards I was replacing an a/c and heat system in
one that had gotten about 3 feet of water. They had the drywall removed
4 feet high and I noticed that several interior walls were built just
like you are talkiing about. House was about 30 y/o at the time, so I
guss they never had any problems. Larry