Edit # 2 - You might want to get a "cuppa" your favorite as this has, again, become a book... So SAD - icons & other things still grayed out, so couldn't attach any... LOL.
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It sounds like your run has no bedding, which you then cover the coop cleanings w/ dirt. So - can you get wood chips? Delivered? If you do ChipDrop, they have a tendency to drop large loads - which you then need to move. Maybe work w/ an Arborist or check both CraigsList & FB marketplace for anyone who has chips available.
@aart has pics of ramial chips, which are better if you can find them.
@gtaus uses shredded cardboard & has started adding shredded paper as in junkmail & bills.
@DobieLover, I think uses combo of leaves & chips
Other items for the run - hay, straw, pine straw & small limbs/cones, shavings, pellets like used in horse stalls, leaves, grass clippings from mowing. Regular paper, hay & straw can mat up & turn slimey, anaerobic & stinky when wet. One way to prevent that is to spread hay/straw/pine straw in yard when you mow - this will chop it up to different sizes. Paper best to use in conjunction w/ other materials. Different materials provides different sizes - allowing for water flowing through & more aeration. This DLM will then digest the poops pretty quickly... If there is scent, add more materials.
Another way to possibly prevent scent would be to put grazing boxes in along the fence (possibly least $$ of next several things). Your grass, flowers, micro-greens, etc will break up "wind carried" scent. May only work @ ground level...
# 2 idea, put in potted plants or a 1-2' raised garden beds about 2' deep, along the full length of the fence.
$3 idea, plant shrubs & flowers directly in the ground. Along the fence.
Do the area closet to Grandma neighbor's house first (w/ all ideas). If you use raised bed idea, when you next clean out the coop, store dirty bedding & poop in feed bags or covered containers, then when do raised beds, use a layer of cardboard & preferably tree limbs/branches, then the "cleanout", then immediately cover w/ next layer of materials based on how deep your beds are... You could add more "cleanout" later by digging a trench in bed (not too close to plants as still hot) & covering trench back up.
Once you do any planting, the seedlings & even older would need to be protected. At ground level to prevent scratching at roots, upper areas to prevent chickens from eating all fruits, veggies, leaves, stems until you/plants are ready. Goats - prob need a secondary fence?
Good articles -
Trees in run -
https://www.facebook.com/share/r/H5YnpdPQwLcjQYqW/?mibextid=oFDknk
Thread 'Plants In The Chicken Run! A Mini Forest For Chickens!'
https://www.backyardchickens.com/th...icken-run-a-mini-forest-for-chickens.1540569/
thread 'Plants for in a run'
https://www.backyardchickens.com/threads/plants-for-in-a-run.1590324/
YouTube -
Sean - Edible Acres. In NY (lots of chicken/compost/garden vids)
Chickens -
https://youtube.com/playlist?list=PLihFHKqj6Jeog3qoYlmhOPt_eElEhNMpH&si=CTRoazLU5bo1CbAu
Chickens & composting-
https://youtube.com/playlist?list=PLihFHKqj6JerKruLfMcxdNKDRHkGxgwwz&si=2ptMkcl7dJusCohI
Parkrose Permaculture - in OR. Small property in HOA, can't remember actual size
Poultry -
https://youtube.com/playlist?list=PLw-_0LHhyR2eRqkIBs4ER-D7nZJpSERhp&si=oCLMJ_YBdQhR584n
Robbie & Gary - CA. Uses totes & buckets for gardens & shows how to continually build/make your own soil. Also other neat projects.
There are others...
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Due to ongoing life issues since I caught covid June 2022, I haven't done much of these. Currently no chickens. Several of my breeding pens have trees growing or heavy duty weeds (pokeweed) through the CP & 2x4" wire hoops. But I've been gathering supplies & will be doing some refurbishing myself, hopefully soon...
Edited to add -
My DLM -
https://photos.app.goo.gl/3Z4ZpfpHr1Nr5DZC8
& add links to YouTube vids