Need Advice on Replacing Boat Shower

The pull up shower diverter to my bath tub unscrewed in my hand as i went to engage the shower, and the remaining hardware fell out of the bottom of the spout. Now i have a bath but no shower. I am hoping this is something i can repair myself but no one seems to have any advice on how i can do so. HELP!! -clueless

We recently had a new bathroom installed. All fixtures, pipes, walls, drains, vents are new. After some weeks, we noticed a small pool of water near the corner on the floor (at the shower end) and suspected a leak from a loose shower curtain. It also leaked through (under the new drywall) on the opposite side of the pipe wall. A cloth placed at the corner of the tub (above the floor, on the outside) remained dry. We placed more caulk at the seams. No luck. Took off the base trim and the next time we showered, the pool of water ran that direction (slightly unlevel floor) more strongly. Drywall wet. Took out a section of brand new drywall (aargh!) to take a look. No leak at supplies, no leak at drain. No leak on inside of cement board, no leak at escutcheons. The plate on the floor where the vent stack goes through is wet, and this is the only place it drips through the floor into the basement. Called the plumber (installer) to take a look. Showed pictures of pooling. While they were here, ran the tub and shower about 10-15 minutes. No pooling but plate appeared a little moist at stack. No moisture elsewhere. They cut the stack and it appeared dry inside as far down as we could reach but could not feel all the way to the drain. No nail holes visible but they didn't want to remove the whole piece of PVC where it went through the floor because it's a tight fit below for the tub drain and will take some redoing. Sorry this is so long but is it possible there is a defect in the vent stack and water is defying gravity? Drain seems to be fine. Could water be running steadily under the plate from somewhere else? The plumbers left and said I need to keep looking for a source (gee, thanks). It only happens when we shower and the grout/caulk all seem fine. A crack in the grout would moisten the cement board, not inside the wall. What next? Thank you!!