If you do rotavate then you need to cover the lot with cardboard to suppress new growth.
You can cover with cardboard and use some of the rotavated soil to weigh the cardboard down. You can also do this and plant through the cardboard...
I think I would rotavate and rake out all the roots that you can; then put cardboard down all over the plot.
If you are thinking of having beds and paths, then put weed fabric down and only walk on the path.
Then you can work on a bit at a time, clear it thoroughly and plant up. Meanwhile; deal with any persistent weeds that grow up through the card - thistles and docks and horseradish seem to be the most rampant on my plot, brambles will also grow straight through and will need digging out from the roots]. Anytime you get more cardboard [or newspaper] put it on where you think it is needed and weigh it down.
For the first season next year you could just plant straight through until you are decided on your layout and how you are going to grow....you still have time this season to buy 10 odd squashes and dot them all over the plot and let them run rampant thus adding to the weight keeping the cardboard down.