Grass seed The rooting will have unearthed lots of weed seeds that will germinate in response to higher light levels. The whole thing will be choked with docks, thistles and nettles before you know it - one year's seeding = seven years weeding.
That is very true.
However, if you put your grass seeds on now, you will have all the docks, thistles, nettles etc germinating at the same time and growing in the grass.
The traditional way to get rid of the weeds is to leave the soil bare over winter so all the undesirables start growing. Then you plough them in in spring, which buries them, and plant your grass onto what should be fairly clean land. The modern way is to let the nasties germinate then spray with glyphosate (eg Roundup) which kills them, and then sow your grass.
Not knowing what machinery, spraying facilities, friendly neighbourhood farmers you have at your disposal, I'm not sure which is best suited to you.
Assuming you have only a rotavator + pigs, I would move pigs onto next field for now and immediately rotavate to get rid of the clods and leave a relatively fine surface. If you don't break up the clods they'll stay on the surface and you'll keep tripping over them. If the weather stays mild then a lot of the weed seeds will then germinate so you could then put the pigs back on it for a few weeks to demolish the weed seedlings.
Or just keep rotavating throughout the winter as a new weed covering grows. Then hopefully by spring you should have got rid of most of the weeds ready for reseeding.