Don't put the input filter on the output, you'll just end up blowing the dust back out of the filter. Just throw it out and use your output filter as the new input filter. Don't bother with an output filter anymore.

Also, it's quieter with two filters because of course it is. It's blocking the air and also blocking the sound as well. But it's really just doubling the resistance to the whole system without providing any meaningful increase in filtration.