Add gypsum to your soil before tilling. We have clay here too, and while I don’t till, just add it every year to the garden, over time it has helped considerably.I finished cleaning out my deep litter coop for this year, the bottom layer was so rich and dark and composted so deep tilled it into the garden. My soil is a lot of clay so while i'd rather do the no till method, the soil gets so hard and compacted there's no other option. Maybe eventually with continuing to add chicken coop compost it will get to where I don't have to till. It's a large garden so that might take a while. Made rows in the open part and cleaned up the few raised beds and added some chives into the bed with the oregano, thyme, sage and mint. Planted some new things - golden amaranth, broom corn, japanese hull less popcorn, bok choi, broccoli raab, this year in addition to the staples - peas, kale, radish, collards, peppers, a few cherry tomato, basil, parsley, summer squash, pumpkin, watermelon, carrots, marigolds. Didn't plant green beans this year. Trying to grow only things chickens can eat so when I let them in to clean up later in the year there's no problems. I know it's a little early for some of the warmer weather crops for here in western PA but I've got squash seeds coming up from one I left there last fall so even with a few chilly nights the soil seems to be staying warm enough for them to grow.
There's just something so satisfying about looking over a freshly planted garden with all the neat rows (and no weeds!) and all the expectation of the good food to come. I thank God every day for having the space and ability to grow a nice garden and raise chickens.