Any photos of your current run set up? Is the run in a lower spot in the yard? How is the existing drainage?Thanks. It's pretty wet in their run and I think I do need to develop dryer ground. Not sure how. But as soon as I have a dry couple of hours I need to clean the coop and they'll get a couple of inches of fir shavings. I thought about some gravel, but I think that sounds a little boring for the chickens. I can't cover the run for a while, so if you have any temporary solutions I would love to hear them. Right now I am relying on their common sense. They like to forage in the grass of the yard and I try to give them 2 to 4 hours a day out there. When they are in the run they stay under the 4 square feet or so of dry ground I provide under the sheet of plywood I put out.
Gravel is a bad idea, it can cut up their feet and once poop dissolves into it, if it can't aerobically compost it'll start stinking.
Do you have access to wood chips, not shavings? Provided the drainage isn't a problem, it's a great way to help control mud and you can build it up a few inches to help provide a drier, more stable surface to walk on. I use deep litter with a base of wood chips: https://www.backyardchickens.com/threads/prepping-deep-litter-for-fall.1599199/ I have good drainage but we do have flooding sometimes, the run drains faster than any of the surrounding area because of the chips.
Temporary covered spots should work fine to provide shelter in lieu of a roofed run for time being, or long term, as long as mud/drainage isn't an ongoing issue.