For Idea 1, maybe another option would be to: remove the existing sheetrock;
sister 2x3 studs next to the existing 2x4 studs; cut the existing 2x4's down
to the level of the 2x3's with a circular saw and/or Sawzall; the
re-sheetrock with 1/2-inch sheetrock. Or, if you have access to both sides
if the existing wall, maybe tear it down and rebuild it with 2x3's and
sheetrock both sides with 1/2-inch sheetrock.

A variation is to remove the old drywall and add your "sisters" so that
they are 1/2" below the studs. Cut the new drywall to fit between the
old studs.

On the finished wall you wall have 1.75" of wood and 14.25" of drywall.
The OP can either paint everything the same color or use a different
color on the wood.

Alternatively, set the drywall base 1" behind the studs. If 2x3
"sisters" are used, the OP could use 5/8" drywall. Small sections of
drywall might "flex" a bit so the extra thickness might be helpful.