I have a hardware cloth floor in the yard part of the coop.
I use pea gravel on top & spray it out daily in the summer. In the winter I put a layer of straw over the pea gravel to give them some insulation under foot.
I have had no trouble with their feet, and it is easy to clean - even in the cold winter months.
To really get the gravel clean I rake it through several times & hose it out in between. My coop is raised up a bit to allow for drainage.
This spring I am cleaning out all of the pea gravel & putting in new. The old stuff will get cleaned & used for a raised area under & around their pool in the big duck yard.
I think river rocks would work well for you.
I used 1/4" hardware cloth, and replacing yours may be expensive. You could try adding some to the lower section in the yard, and maybe doubling up the 1/2" stuff by bisecting the 1/2" sections with one another, if that makes any sense.
Good luck to you. You'll get lots of good advice & points of view here.
The coop building process is so confusing for me, too. Very anxiety inducing. The whole first summer I had my ducks I would wake up in a panic thinking the ducks were getting eaten by something, and had nightmares of foxes & raccoons. You get over it.