Bagless vacuums with filters are a pain. The filter clogs. So does a bag, in fact.
What you want is a CYCLONIC vacuum... but they're expensive. Like, a good bagless vac with filter can get into the $300-$500 range. A good cyclonic will start there. Cyclonic vacuum works by spinning the airstream such that heavy particulate goes to the outside from centrifugal force, with a vent in the center column. Because the debris goes to the outside, it doesn't go out the vent. Because there is no filter, air flows freely through the vacuum unit--maximum vacuum power is achieved at all times.
My solution to all this?
Something like this. Pipe the exhaust outside, because even a HEPA filter only catches 30% on each pass--you'll spew the rest of the garbage into the air. Mold spores, dust, bits of dust mite crap, bits of dust mite bodies, yes the filter traps these things but even the stuff in the actual Manhattan Project didn't catch 100% of plutonium dust every time--it caught a third of it, and the air recirculated so much that 2/3 of 2/3 of 2/3 of 2/3 of 2/3 ... is eventually all of it.
