I understand the clean up of dog hair was your question but you might want to make sure that the amount of shedding is normal. Something else may be going on. Healthy dogs do not shed all year long. I have a lab and we have had major problems with her shedding.
We took her to the vet and ask about the issue on a routine visit. The vet stated she could be allergic to her dog food. She suggested trying a food that had Chicken as the first thing on the ingredient list and to stay away from brands that have Beef, wheat,corn and other fillers as the primary ingredient. We changed her food and wow what a difference it made, coupled with weekly brushing I took a major problem for me and my dog and fixed it. We started with Rachael Ray's Nutrish it took a couple of weeks but wow what a difference.
Bleach and a scrub brush.
Do not wipe the mold this could make it become airborn. Spray it with bleach and it will disapear with out touching it. Then paint over with kiltz. However you need to be very careful not to disturb the spores and inhale them, this can cause many health problems.
We have always drilled holes in the tops of the stumps and filled the holes with rock salt, it works but it does take some time to rot the stumps. I have also read putting Charcoal on the stumps to slowly burn them out works, but I have not tried .