repairing water spot/damage on ceiling
I'd like some advice on fixing this problem. We have a 2 story house; the master bath is above the family room. I noticed about 6 months ago or so that water was somehow leaking out of the corner of the shower stall (probably because the door wasn't closed tight) and the vinyl outside the stall had lifted. I dried it off and recaulked. Around the same time, we noticed a baseball sized spot on the ceiling below, which coincides with the placement of the leak. It's soft, but not wet.
We're hiring a handyman because hubby doesn't want to deal with this. One guy suggested a simple 6"x6" patch that he would tape, seal with joint compound, and spray with texture. Labor alone will cost $350, which I thought was pretty pricey. The second guy, who has a plumbing background, said it looks like I correctly stopped the leak, although he will look more thoroughly once he removes the damaged portion. He is suggesting putting a piece of backer of some sort, i.e. plywood or sheetrock, up inside the ceiling to cover the hole, then screw a patch into the backer, then use joint compound, etc. This sounded more sturdy/stable to me, and I am wondering what your thoughts are. The second guy will be giving me a bid by tomorrow morning. Both companies are licensed and members of the BBB. Thanks!