You can lift your combined coop & run off the ground onto a base of single cinder blocks or 2 cinder blocks high. That will give you the depth you would want/need to do the DLM in the run area (s).
Others have addressed building your coop larger, so I won't.
What state do you live in? What type of climate do you have?
I personally don't like sand - but due to lots of rain and humidity here in the "sandhills" of NC - sand with any amount of chicken feces stinks badly and attracts flies. No matter how much you are able to scoop it out (& there are lots of ways to make scoops that will get most of the poop out), small bits of feces remain behind in the sand. When wet, it will usually smell bad, though I've had some say it doesn't.
The main thing with DLM is to get varied and different sized materials. The same type and same size material will mat down and will also start to stink as it goes aerobic - blocking oxygen from moving through. It will also turn slimey and slick - posing slipping hazards for humans as well as undesirable conditions for the chickens.
We have used a variety of materials - some from our property and some brought in. Straw, hay, pine straw, leaves, veggie/fruit/garden waste, cut grass, cut weeds, wood chips, bills/junk mail/paper/cardboard that I shred or bring home already shredded. Pics of some of that here -
DLM
There are a lot of threads on sand, bedding and DLM on BYC.