... and "fifth-ed, sixth-ed and seventh-ed"
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I am single trenching going down a foot and a half "
That's quite deep? The depth of the Spade or Fork (a "spit") will do, if you want to go deeper than that then "double digging" is the norm - that prevents mixing the lower sub-soil with the better top-soil.
Roughly dug now is not going to break down into a beautiful tilth
Anything that had the frost on it should do better. Shuffling down the seed-row in your wellies on a nice dry day will break up the clods (you may have to do it again a little while later after some rain then more drying sun) and work the soil with a stiff rake.
But my take, as others have said, would be:
Rotovate to break it all up (you'll need to dig it first, or hire a very beefy cultivator to break up virgin ground). For ground that has been hand dug a little Mantis Tiller will do a great job of smashing up the clods - perhaps you can borrow one locally?
Raise plants in modules / small pots (if you can, and the hassle is not too great?) or if you are flush! then buy some small plants from the garden centre. You can then make planting holes in your rough-dug plot, with a trowel, and take the time to smash up enough soil - say a 6" diameter "vertical tube" - so that the plant has enough soil comfortably around it to get established.
Covering the plot would help too. Cardboard, newspaper, mulching-plastic (weed suppressing membrane). You can plant through those (which will keep the weed in check) ... they will help keep the surface more moist, and that will make it easier to work the soil.
I would not use carpet - it falls to bits and is a nightmare to remove, and may well have noxious chemicals in it. Our old carpet was used as a mulch for a hedge - no intention of ever removing it, or eating the hedge!, but I've avoiding using carpet on the veg plot.
Potatoes will help clean the ground. They have to be earthed up as they grow, and the act of doing that moves the soil about through the season, which also tends to help break it up.
Trailing things like Pumpkins / Squash need very few plants, and cover a large area. Often a good choice for a new plot that is covered with plastic / cardboard. You can make a planting hole for each one, put plenty of well rotted manure, or compost, in and the condition of the rest of the soil doesn't matter very much. You will probably only need one plant every 6 feet! and the covering of plastic / cardboard will stop the weeds growing and make the soil much easier to work next year.
I also liked the idea of runner bean (or climbing French beans if you prefer them). You can dig a trench in your nice newly cultivated soil, again put some rough compost material in there (well rotted farmyard manure is ideal, but even shredded newspaper will help) that will absorb the water when it rains, and the the beans will be very happy! They will put some Nitrogen back into the soil which will help for next year.
Having said that, I think it is important for newbies to plant what they enjoy eating. No sense having a disastrous crop of something that you don't like in the first place!
I'm looking forward to the disappointed looks on the naysayers faces when you succeed!