The only problem I see and it is a relatively small one; is that swales generally need to be dead level. It would be difficult to achieve that with hogs alone. I think your ideas of how to try sound reasonable though and if the hogs do the majority of the hard work you should be left with only some small adjustments to get to level.
Right, I was thinking the planting stage post-disturbance would be when you do the final adjustments to the swale making and the pigs just get the bulk of the dirt moved.
I was also thinking that the pigs would mostly disturb the soil, but rain would move the disturbed dirt down hill, and the dam would prevent it from washing away entirely. Water is an excellent leveler.
A slower method would be to plant sunchokes (Jerusalem artichokes) where you want the hogs to root up let them grow and then let the hogs self harvest the tubers.
Our pigs don't eat sunchokes, even cooked ones put in their slop, they ate around them! :/ We have a breed that doesn't do a lot of rooting, maybe we'd have to find a different one for this application. They do rustle around in the dirt looking for grubs and nuts, which is why I thought multiple years of looking for acorns could move enough soil. Plus, on my particular site, we'd be doing this in the woods, and I'm not sure I want to introduce such a persistent species to my local forest ecology. I like the idea of spreading out annual seeds for them to find, though.
Might work with other pigs in other locations though, I like the idea!
Even without fencing, many animals tend to graze on the contour and will build up terraces.
I was thinking you could capitalize on this natural tendency and control it with fencing.