Welcome Pier:
This is an interesting question but to give you a good
answer Some more information would be helpful. You stated the last frost was Oct. does that mean you are in the southern hemisphere?
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I have a section of my land that has clay soil that I am experimenting with because it is ideal from the standpoint of being sub irrigated; That is the sand area above slope drains into it and keeps it moist all summer wen it seldom rains.
https://www.youtube.com/user/eOrganic has several videos that suggest cover cropes for penetrating compacted soil. one of the ingredients was the large radishes. An extension agent ran an experiment on a neighboring farm with foraging radishes. During the farm tour they let the animals in. The cows ate the tops, the sheep ate down below the soil line and of
course the pigs rooted them out and ate the whole thing.
It may be best to have a moveable pen and have them clear it quickly then plant that area while they clear the next. there would probably be less compaction that way and they would not just clear their favorite things and leave the less desirable probably more problematic things behind. If your cover crop is more nutritious for the pigs then the second pass would help fatten them up for slaughter.
Dig a test hole and see how much soil there is above the subsoil. I have found a broadfork helpful in breaking the compaction to get
roots deeper quicker. Right now I am using a
chicken tractor and if I break the soil then the
chickens are able to scratch the soil from the edges where they were not able to scratch into the clay surface.