Sounds like a plan. Without seeing the area, I can't say the rib is there, but if you have a row of rivets outside and inside in the same place, the rib is there. The closet may not lend much, if any, support. Check inside the overheads to see how the overhead is riveted to the wall. Both the Minuet and the Caravel
have the overheads hanging from the wall with the closet wall as a support/stabilizer at one end. The other end is supported by channels riveted to the wall fastened to an end piece for the overhead.