Any kind of organic compost will work. What I would do is remove as much of the peat-based mulch as possible and pile it up somewhere. Then, spread compost, manure, shredded leaves, anything that you have, anything organic...wood chips...whatever.. over the bed (best if you can deep water it first). Compost (as long as its well rotted) is the best mulch you can find and it will help the soil. You could try mixing the removed peat-based mulch with the compost, either before or after you spread it, but I'd go very lightly with the peat stuff. I know just what you mean: I did the same thing and after the peat dried, the water beaded up and rolled off! I removed it all, tossed into my general compost heap with leaves, grass clippigns, whatever etc. and let it all rot together for a year before I was able to use it.
And same here, what Kyla says: We're hoping and praying for rain for you all every day.
OH, this just occurred to me. I read that in drought conditions, laying large pebbles or flat rocks over the soil around the base of plants will help conserve moisture. The rocks can also act as "dew catchers".
