This was step 1.
It took quite a while to find someone willing to take a free 10 year old pomegranate tree, but we managed to get it done today. Now that corner of the yard is wide open, and spending the day out there digging in the mud really jumpstarted my itch for gardening this year.
The plan is to move the raised beds/raised boxes/benches over to the other side of the yard. We'll have to take most/all of the dirt out in order to move them, but that's fine, it'll give us a chance to get some compost mixed in/etc.
Then! Then I'll move/reroute/stub/etc. the sprinkler/irrigation lines, extend the cement pad with some gravel, level it all out, and get a shed!