Structurally that's a verysimple span, especially with the end walls done up. Prop a ridgeline up for the wet mud and give it a good week before removing. The longer you prop and proper cure the better obviously. The closer to catenary the stronger, but it ain't that important with your spans for goats. I've done less radius than your Roman arch at 20' span, simple Hardware cloth and Cattle panel armature. Bomber strong.
If you go Without the end walls, I'd thicken the edges. But you could easily do end walls and just frame out doors incase you want to close it up. It'd be more versatile.
You could hypar, but I find it more expensive for me locally than good FC even when buying mesh. I also find it slower. For FC, I suspect you'd need 3-4 bags of fresh cement and then have 30 gallons mason sand (redi mix or maybe pit) per bag. Haul in pickup.
And you already have the best mesh to use installed. This fc will handle goat impacts, kicks, playing better than hypar too. Hypar over this doesn't use the metals potential.
Hardware cloth (I like 1/2" best...) and cattle panels are my preferred armature for FC vaults. And you already have some installed. An inside lath layer (4 sheets per panel is perfect for $20 52"x16' panel, wired tiiight to panels would make a nice mesh system for your
project. Stucco netting or lath also have their places in FC.
The drier the mix the stronger and more
water proof, but harder to apply.
That could handle a FC footer. Or tie pounder t posts into the inside corners. Or some simple deadmans buried. FC won't fly away or flex in a vault like hypar in the vault shape.
2.5-3:1 mix for fc
If you are in a wet climate with freeze thaw cycles, add a sealer before winter.
Have fun. You may like it
enough to drag it out of the pasture for a studio, just a warning.