I had a terrible year one year in the lambing pens, weather appalling, couldn't get anyone out. Watery mouth and worse was rife, we lost a lot of lambs we shouldn't have lost.
That decided me that deep litter and lambs do not go together. Cleaning out the pen thoroughly, letting it dry properly, disinfecting / liming before next use is my way now.
So I would advocate that in your cade pens too. Yes top up on a daily basis but do a deep thorough clean of every pen once every 7-10 days. If you've got 130 pets in pens of 5, you've got 26 pens? So if you do two or three each day, you do them all over the course of 10 days. If you do 4 a day, you do them all in the course of a week.
I take the point about not being practical to disinfect wellies, but try to organise your setup so you don't have to go into the pens very much at all. I reared a pile of cades every year in Cumbria and only really stepped into the pens to clean them out. All feeds and water were accessible by leaning over from the outside.
If you simply have to walk into the pens, start each round with disinfected wellies and go into the most recently cleaned out pen first, then into the next most recently and so on. So if there is infection breeding over a number of days, you're not taking it from a dirty pen into a clean.
How are you feeding them and where does the spilled milk go? It's a good plan to clean up the spilled milk and the ground it's fallen on more often than doing the whole pen. Most bacteria lurve milk as a growing medium
As well as your wellies, think about your hands. What are you touching in each pen and what do you touch in the next? If you've got shitty lambs, don't touch them or anything they've touched (as far as is practicable), and wash your hands (or wear gloves and wash or change the gloves) before touching another batch of lambs.
I'll probably have some more ideas once I know a bit more about how you've got it organised, how and what you feed them, and so on.