Dandelions mean compaction. Clover means low fertility. Neighboring plot looks like high clay content.
What tools do you have to work with?
I had a similar situation on my own garden, what I did was to use a subsoiler first as deep as I could get it to decompact the soil. Then top dress with manure, and
compost, about an inch over the whole garden. Then till it all. Then make permanent raised beds by shoveling all the soil from the path to the bed. Paths got cardboard or newspaper and then sawdust or wood chips or straw as deep as I could afford. Beds get covered with tarps if you have time, or left bare for a week then flame weeded if you don't.
Major disruption like tilling is OK ONCE, especially since you are changing the biome so much it will be disruptive anyway.
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