I think you've got to find them trimming trees locally and stop by and say 'hey can you dump those chips at my place?'I'm thinking that I'll probably end up doing deep litter in the new higher run in the end. My worry for doing it with the run at its current level is that the ground might be too wet underneath. I've read horror stories of "deep litter gone bad" because it was too wet underneath. Your earlier recommendation of wood chips would probably do the trick but a delivery of chips would still have to wait until the ground is firm. I'm going to watch the ground and see how bad it gets. If I think I can do deep litter right on top of the ground with the run at its current level then I might not have to raise it at all and will do deep litter on top of chips.
As an aside, I don't know where people are finding tree services willing to unload unwanted chips for free. Everyone I've called wants to charge me for the chips and delivery. Three yards was going to cost me $75 delivered!
Several folks in my area have had that done...some to excess, ya gotta tell them when enough is enough.
I have fairly sandy soil in my run, it can puddle in a hard rain or at snowmelt, but usually drains away within a day or so.
The stink when wet is atrocious for sure...I started adding some cut grass and leaves gathered with the mower late last summer and it made huge difference.
Definitely reduced the smell and gave the chooks something to scratch around in instead of the bare dirt.
I did go slow in adding material as I didn't want it to be too deep and go anaerobic and just kept an eye on it all.
A good balance of size, shape and content of materials to avoid compaction is a very good idea.