Hi Grace. Welcome.
Your ideas for crop rotation sound good, but I don't know if they're compatible the way you've arranged it. Also, with that high a soil pH, you're going to need to do some amendment.
Most crops prefer a slightly acidic soil, and potatoes prefer it more acidic, like between (if I am remembering correctly) 4.5 and 6.5 pH.
Were I you, I would see if there are any alkaline-loving crops you might plant at the start. I am not positive, but I think asparagus is one such, and alfalfa, but you
should doublecheck that. Growing alkaline-loving crops will cause the acidity of the soil to drop over time. Also, alfalfa is deeply taprooted and a host to nitrogen-fixing bacteria.
If you are determined to grow acid-loving crops, then you will have to amend your soil pH.
Do you have the results of a soil analysis that you could show us? That would help a lot. Is your clay soil calcium deficient?
In any case, I would suggest that you find a good source of organic matter.
Wood chips would be great. I would drop them right on top. If you had
compost, I would add that too, right on top. If your soil is calcium deficient, I would add gypsum. I would then broad fork it all such that some of the rock dusts and organic matter sift down a bit into the soil. Incidentally, if you have access to
coffee grounds, I would drop those on top, too, before broad forking. Worms love coffee grounds, and if you're lucky, they will be doing most of the grunt work for you.
In terms of crop rotation, I like to look at companion planting lists after I have chosen the key species I want to base my plantings around.
If you are going to grow corn, I would suggest looking at the Three Sisters planting technique, whereby you grow corn primarily, which acts as a support for pole beans you grow in the same spot, which host nitrogen-fixing bacteria to feed the corn and the squash/pumpkin, whose broad leaves act as living mulch, cutting down soil evaporation and sunlight availability for weeds.
I have heard that the Three Sisters are primarily good for producing dried crops, but spacing the corn on 18-inch centres, I find I have
enough room to move around individual stalks to harvest the sweet variety. At worst, I have found that my beans dry out, so I have taken to planting them with that purpose in mind.
I have heard that there are disease issues surrounding following corn after solanaceae, and potato is one such. I would look into this.
Pumpkins are heavy feeders. I don't know if yours will do well following your corn and cucumbers, which are also heavy feeders. If you plant clovers in between rows, that might help, but I would make sure I was planting a nitrogen-fixing bacteria host crop along with my heavy feeders.
If you could let us know a bit more, the suggestions you get will be more useful to you.
In any case, please let us know, and keep us posted as to your progress. Good luck!
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein