I think you will be happy with those 18” x 20” nests. The bigger the individual nests, the more hens they can handle. A general rule of thumb is that a 12” x 12” nest can handle 4 hens. A bigger nest can handle more. Three nests can easily handle 15 hens, but if you have room and the materials, more won’t hurt. I do suggest you make the lips fairly high, 4” to 5” not being bad. If the lip is too low, the hen can scratch out the bedding or any eggs already there when she is adjusting the nest to get it just right for her egg.
Kelsie, I had an experience last summer that made me a much bigger fan of larger nests. I let a hen hatch in a nest made from a cat litter bucket, not a box but the plastic bucket the litter comes in. The dimensions are 9-1/2” x 11-1/2”, but I had it at a 45 degree angle to hold the bedding in and it had no top. My full sized hens had no problem laying eggs in that. But when chicks hatched, the first ones to hatch climbed up on top of the hen while the later eggs hatched. The hen was sitting so close to the edge that when the chick slid off Mama’s back, it fell out of the nest. My normal nests are 16” x 16”. In those the broody hen is far enough away from the edge that when the chick slips off her back, it falls in the nest. Not in a small nest. I agree with you on hens squashing in there, I often have three at a time in my nests, but to me there is an additional reason for larger nests. Fewer problems when a broody hatches.