If the microorganisms have more surface area to feed on, the materials will break down faster. Chopping your garden debris with a machete, or using a chipper, shredder, or lawnmower to shred materials will help them decompose faster.
If you find lumps in a can of paint that you need, you can “push” them out. Cut out a circle from a piece of wire screen slightly smaller than the can’s inside circumference. Put the screen circle on the surface of the paint. With a little help it will sink to the bottom of the can, taking the lumps with it. Another way to salvage lumpy paint is to strain it through an old nylon stocking.