I'm certainly no expert on DLM, and I completely defer to Bee on this, but it occurs to me that this isn't an average "how do I deal with excess moisture" problem but rather an "I need temporary flood management measures" situation.
Rather than trying to find a long-term solution for what seems to be a short-term and exceptional problem, maybe a stopgap solution is the answer. Rather than risk throwing down more good (bedding) after bad, might it be better to toss all the coop bedding into the run, throw down a temporary floor of pallets and wait for the flood to pass. If this is truly an aberrant weather pattern, just make some temporary modifications to get the birds out of the wet and ride it out until it passes.
Rather than trying to find a long-term solution for what seems to be a short-term and exceptional problem, maybe a stopgap solution is the answer. Rather than risk throwing down more good (bedding) after bad, might it be better to toss all the coop bedding into the run, throw down a temporary floor of pallets and wait for the flood to pass. If this is truly an aberrant weather pattern, just make some temporary modifications to get the birds out of the wet and ride it out until it passes.