That sounds like my situation. The wire deck idea is very clever! If it were only for a few weeks and they were only on it when they chose to be, I wouldn't be risking bumblefoot, right?Sometimes when the soil has been compacted and there isn't much by way of organic matter in the soil, it becomes like a solid mass that sheds water. It's fairly common in permanent barnyards where there are no roots in the soil anymore and the topsoil is constantly compacted by foot/hoof traffic. Sand actually makes it worse as it percolates into the soil and makes something akin to cement.
If you want to improve that soil, you can partition parts of it off from the animals and amend it with good compost and then plant some cover crops on it -- like clover, bell or fava bean, etc. -- when that grows you can either chop it into the soil, or let the animals back on it to graze it down and return it to the soil with their manure. The key is rotation so that each patch of soil gets a break from having every scrap of organic matter picked clean off of it and tramped down. If you have to have animals on it all the time, you can also construct wire covered decks that you place over "resting" soil, which allows plants to grow but keeps the animals from picking them right out as they can only access the portions that grow above the wire. If the "decks" are of manageable size, you can move them around as needed.