Dam, Swale, or Hugel - Which one?

So I am having a rented excavator delivered to my property next week. All my swales, hugels, and dam locations are marked, now all they need is dirt. However, I only have the weekend and I am afraid I won't be able to get it to all. So,  I ask you the good people of Permies what tasks should I prioritize. I foresee four main courses of action.

1. Dig swales first... all 14 of them
2. Dig dams first across an erosion gulley. This would be about five dams spaced 15-20 feet apart with drains. I estimated the gulley's drainage area is two acres and comes from off my property so that drainage area is inaccessible to me. Important note: this erosion gulley is uphill of the swale area and none of the swales would reduce the water volume.
3. Hugelkultures first. I have three of them prepped with wood and slash. However, the wood is juniper and pinyon and thus not optimal.
4. Dig main swales first (about four total), then dams, then hugels.

Some details about my land (to limit "it depends" answers)
Soil:  Silty clay.
Biome: Pinyon-juniper transitioning to prairie.
Annual precipitation: 18 inches
Most in a 24 hour period: 3 inches
Average slope of erosion gulley: 13%
Average slope of swale area: 5%
Goals: Reduce erosion, build soil, retain as much moisture in land as possible and provide suitable sites to plant siberian pea shrubs, locusts, and berry bushes for my chickens to forage.

Thanks for taking the time to read and please share your thoughts.

I recommend doing all 14 swales, then the dam. given the limited amount of rainfall that you get I would go for buried hugels in a depression vs towering 8ft ones.

Actually is it possible for you to fill the gully with the brush pile, vs building hugels? Then you would be able to build brush dam.  Do you plan on building a dam across the gully where it enters your property, and then have all of that extra water from above you soak and enrich you land as it spreads across your land vs gets concentrated in the gully.

This would be about five dams spaced 15-20 feet apart with drains

S bengi's idea of brush dams is worth consideration, but I want to talk about the space between the dams in the erosion gully.

The toe of the upper dam should be at about the top of the lower dam.
Build from the bottom and have rocks etc so that it reduces the chance of a washaway.
Plant all exposed dirt with locals seeds that will grow quick and hold the soil.
maybe add some seed balls [ clay ball made with clay and local seeds for low storey plants]

The toe of the upper dam should be at about the top of the lower dam.
Build from the bottom and have rocks etc so that it reduces the chance of a washaway.

Thank you. I didn't think of that. At 13% slope, the gulley is dropping approximately 3 feet for every 25 feet of run. So you're absolutely right that I need to space them 25-30 feet. Secondly, I need multiple ponding areas (like an icecube tray) in sequence to take the anticipated amount of water which I calculate to be 50,000 gallons in a severe rain event given a 25% absorption rate.

I have used brush walls. They build up silt for which I am grateful, but the water continues to flow around them and hollow out the sides. The majority of water is still leaving my property to join the Arkansas river's march to the sea. I want to stop and infiltrate all of the water.

The ultimate plan is to use swales slightly off contour take the water from the gully and spread it out to your entire property. Preferable right when it enters the property. Vs right when it ends your property