I've tried kind of terracing it, but the girls still scratch the mulch to the low point.
It's about 185 sq ft for 8 hens
photo? what did you terrace it with?
Chickens like green matter. If they're stuck in a run because there's no room to let them free-range, they're going to eat stuff like the clover first and anything going to seed, then the grass and then the weeds last. Nothing you can do about it. If you're worried about it being muddy too much when it rains and during the winter, then best to pour a concrete slab and throw a flake or two of some good green hay for them to munch on once or twice a day depending on how many birds you have.
I like that you've given your birds 24sqft a piece. That is well above the suggested 10sqft minimum.
You can build some sort of box just inside the fence of the run to level it -- and add sand.
If you don't like the run because it seems like the birds are bored -- add toys. Hanging cabbage, flakes of hay, outdoor roosts, etc.
They'll constantly be scratching any 'sand' you put in there, out. You'll be adding sand all the time - that adds up to throwing money out the door. It'll be harder to clean, meaning you'll have to constantly cat-scoop the poop by bending or on your hands and knees. Getting all the old feeds, and treats and things that are not 'scoopable' will be a PITA too. It *will* eventually hold more 'junk' than you want it to and will begin to stink. Sand has its uses, but IMO not in a chicken run unless you just don't care about any of the above and don't mind the extra work it involves.
A concrete slab you can 'broom' to make it so it's not slick. Then when it comes time to clean, a hose is all you need. If you wish, cut a big 4" or 6" diameter PVC pipe the length of the run, wash everything into that and have it so that it 'drains into a 5 gallon bucket. Empty that bucket onto your garden/flower bed/etc. It also cools the concrete and in the summer the birds really enjoy it as it helps cool them also and you know that it's actually *clean*. You can even put the birds up in the coop temporarily and use a pushbroom and soap and water if you need to clean any more for any reason than plain water.