Dito on the allergen washes for clothes and bedding.. carpet and furniture shampoos..
IT is a must to allergen cover your matresses and pillows! Type of vacuum.. I use a hoover wind tunnel and it works well. We have two dysons in my family as well.. don't notice much difference in after effects.
Also by a steamer.. we use a hoover as well and I wash my carpeted surfaces every two weeks. This helps tremendous.
Invest in rubber maid bins.. if he want to keep it.. he has to store it and stack it.
Throw away excess paper too.
Best of luck.. I understand the pack rat syndrome.. add OCD to the mix and thinks get really hairy.

MG