Thanks everyone, for your support! All seems to be well at the moment. Separate coop and makeshift run within the chook yard. And yellow peep seems to be fine!
The main trouble of incubating in the run is hens trying to steal your broody hens' nest. Or the setting hen becoming confused when she comes off the nest and she then gets back on the wrong nest. You can be quite sure that a new mother hen will do all of her babies' heavy fighting for them.