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.
To save trim during remodeling, use two small, flat prybars. Slide the thin end of one behind the trim, pull, then insert the second in the space that opens up. Alternate pulling each bar to inch the trim off. If finishing nails protrude from the back, use slip-jaw pliers with a rounded top jaw to pull them through.