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Hi Stacey,
You don't need a bulldozer but a heavy duty rototiller would probably be a good thing to rent for a few hours.
My husband was transferred often before he retired. We moved nine times during our first 25 years of marriage and I had landscaping challenges in each of our homes. Here's what I did.
Make a list of the things you want incorporated into your yard space then prioritize your dreams. Work on a small section of your yard to fulfill one important goal and do not work in any other area until you are totally satisfied with the completed project. I call this pocket gardening. The first pocket could be a seating area, a water feature, or a raised bed.
By focusing on the exposure in that one area, amending the soil and choosing plants that all have similar water needs, you can choose a combination of pleasing color, fragrance, and/or texture variation, etc. With regard to budget, design and time management for the project, it's much less of a burden to be re-landscaping a corner or small strip of your yard than taking on the whole thing at once.
You could buy 1 section of pre-fab fencing to delineate the back of a pocket garden just beyond the patio by your back door shown in your photo #4. The gardening area could be as big or small as you would like.
Hope this gives you some ideas and some motivation to get started! Please visit my Forest Gardening yard and vote for me if you like what we are doing..... one project at a time.
Janet Drake