Welcome to BYC!
Definitely should correct the poop in nests issue......
......but that probably wouldn't keep them from laying in the nests if they wanted to lay there.
Signs of onset of lay---I've found the pelvic points to be the most accurate.
Squatting:
If you touch their back they will hunker down on the ground, then shake their tail feathers when they get back up.
This shows they are sexually mature and egg laying is close at hand.
Combs and Wattles:
Plump, shiny red - usually means laying.
Shriveled, dryish looking and pale - usually means not laying.
Tho I have found that the combs and wattles can look full and red one minute then pale back out the next due to exertion or excitement, can drive ya nuts when waiting for a pullet to lay!
2 bony points(pelvic bones) on either side of vent:
Less than 2 fingertip widths apart usually means not laying.
More than 2 fingertip widths apart usually means laying.
They may be low on protein, layer feed is usually the minimum of 16% and the other foods you are giving is diluting that. Maybe cut out the scratch and scraps for a few weeks to see if that helps...or switch to a higher protein feed to offset the other foods.
I like to feed a 'flock raiser' 20% protein crumble to all ages and genders, as non-layers(chicks, males and molting birds) do not need the extra calcium that is in layer feed and chicks and molters can use the extra protein. Makes life much simpler to store and distribute one type of chow that everyone can eat.
The higher protein crumble also offsets the 8% protein scratch grains and other kitchen/garden scraps I like to offer.
Calcium should be available at all times for the layers, I use oyster shell mixed with rinsed, dried, crushed chicken egg shells in a separate container.
Animal protein (mealworms, a little cheese - beware the salt content, meat scraps) is provided during molting and if I see any feather eating.
You may need to confine them to coop and run to see if they are laying and to habituate them to using the coop nests.
Free range birds sometimes need to be 'trained'(or re-trained) to lay in the coop nests, especially new layers.
Leaving them locked in the coop for 2-3 days can help 'home' them to lay in the coop nests.
They can be confined to coop 24/7 for a few days to a week, or confine them at least until mid to late afternoon.
You help them create a new habit and they will usually stick with it. ..at least for a good while, then repeat as necessary.