My dearest kaleuns,
I can't make Longer repair times mod work, no matter what I do. Just to try it, I got deliberately depth charged myself by a Black Swan. I got some minor damage in bow compartment, flak and deck gun, stern compartment.
I slipped out of that trap and commenced repair operations. All damage was repaired in 2 minutes!
For easier understanding, let me show you my activated mods: (click on the image for larger version)