One important note about compaction pigs/dozer. There is a wide variance of ground pressure machine wt divided by track contact area. A typical D7 with standard shoes will be 10 psi probably at most. A cat can certainely compact in the proper soils. The operator must understand what he is trying to accomplish. Most cloven feet animals will 3 to 4X the compaction. Thus some brilliant inventor invented the "sheep's foot" compactor.
If you have access to it, I would vote for shooting a few tanks of liquid manure in. No fences and no disruption of the "compacted" soil liner from rooting. I don't know if one of my ponds is leaking or just hasn't settled in from still not having a belly buster rain since a rebuild of it 2 years ago. If I can't keep it full, I am certainly going to give it the manure tank treatment.
