Good question, it has been asked for the last 30 years by people inside the business. Solutions tend to be on the front end, do not create unnecessary LLRW. ALARA (As Low As Reasonably Achievable) is a philosophy that exists primarily in the nuclear field, meeting the regulatory limits is not enough. Whenever possible and reasonable personell exposure, environmental release, and waste volume must be reduced. Processing radioactive waste for the reduction of radioactivity is only possible for High Level Radioactive Waste (spent nuclear fuel) where some of the recovered radioactive material becomes useful product. LLRW must be buried, but it can be processed for volume reduction. Some companies make a living by receiving LLRW, monitoring it and removing the clean material or reducing the volume by shredding it or compacting it. Personal protective clothing makes up a lot of the waste volume and there is a paper suit (Orex) that can be digested and filtered leaving only a fraction of the original waste volume. Waste management in the nuclear field is big business particularly on the DOE side where many of the old buildings and sites (Manhattan Project facilities) are CERCLA sites (Hazardous Waste Sites designated for cleanup) and are far beyond their useful life spans.
By the way "storage" is probably not the right term for LLW each of these burial sites is intended for 300 years of containment at which time the radioactive components of the waste is essentially gone and only the lead, PCB, asbestos and other hazardous wastes are left provided the landfill is licensed for that. Not much different from any other landfill. High Level or "Greater than class C" waste is the only waste that has to be stored until a long term solution is found.