Right now is a great time to clean out your coop floor completely, just rake it out, then add 4" of clean wood shavings and sprinkle with DE. Throw a small amount of scratch on the coop floor every week and you can mix or rake as needed. 4'x4' coop is very small. It is good that your dirty litter is dry and not smelly, that means you are doing a method that works.
Hugh's new litter rotation method:
Start with clean shavings in all three Sections, assuming the coop has exterior nest boxes attached. Sprinkle floor with DE before adding new shavings and also sprinkle on top of shavings:
Day 1:
Section #1: Nest Boxes - 2-3" of fresh shavings
Section #2: 1/3 of coop floor in front of nest boxes - 2" fresh
Section #3: 2/3 of coop floor under roost bars - 4" fresh
2 months: Throw Section #2 old shavings over to #3 and mix (6" total). Throw #1 onto #2. Add 2-3" fresh shavings to Section #1 and fresh 2" to Section #2.
4 months: Repeat 2 month procedure, Section #3 now has 8" of shavings.
6 months and New Day 1: Clean out Section #3 to compost pile. Add 2" fresh shavings + litter from Section #2 to Section #3, repeat Day 1 above, repeat, repeat, repeat. A full clean out of Section #3 can be done at anytime after 4 months or partial clean outs, whatever you decide to experiment with...
Enjoy the flowing system, any feedback? Am I nuts?
--Hugh