I say go for it! As long as you're thinking of going to all the trouble of a rock retaining wall, adding your rotting firewood is minimal additional effort.
Some people see downed
trees or rotting
wood and think: "water!" I see them and think: "soil!" Both thoughts are appropriate for your situation, so you can't lose. Be aware that your rocks are going to be a heat sink in the sun, so put the emphasis on heat-loving plants (peppers, tomatoes, squash, melon - if you have the space) and use plenty of mulch to limit evaporation from the soil surface. Or build your retaining wall from timbers (salvaged, of
course), which won't heat things up as much. Consider harvesting
water from your downspouts to make it through the dry period. Seems you're getting plenty of moisture this spring!
For your back yard raised beds, try planting your more shade-tolerant veggies back there: almost all your greens will love it, and
root crops and beans will put up with it. Try adding a bunch of tap-rooted support plants (comfrey, mullein, daikon) to break up the clay pan under the beds and create root channels for your harvestable crops. These plants will also add biomass for soil improvement, mulch and compost. Plus you can use parts of each for
medicinal purposes or food. Mulching everywhere you eventually plan to plant with lots of wood chips and planting daikon and other big-root-system herbs will open up the soil and give the soil life a chance to come to your assistance. Worms and bugs will only show up for work if they are protected from sunshine and heat, and they'll really appreciate plants that open things up a bit for them.
Good luck!