The DoF angle hadn't occured to me, but yeah you sure could
To clarify: you mean pushing the settler out of your cap right? If so I'd say yes go for it. We need to get at least some economy rolling ASAP.
More military units will just drag us down and traffic jam up, just look at how gummed up and discombobulated Woden and Chevs assault is. With my UU in the field Woden's archers are pretty much nullified anyways (I've seen these guys with Turtle promo tank Field Cannon fire like it aint no thang, think of Black Panther in Captain America: Civil War

) I might even be able to scramble up a battering ram or just take the city back outright before they build walls if they do manage to take it.
Unless another team piles in on us I think this rush will be a temporary setback, not a game-ending situation, and bear in mind that Woden might look a little threatening and in a temporararily weak position to the other teams as well

Also if Woden can't close the deal on this his team is pretty boned. They have done nothing but build military pretty much full-stop, if they don't make significant gains now, their game is unsalvagable. If we hold on and get my UU out, I can already see Woden getting all defeatist like he did in previous games where his plans went awry.
My builder plan would put the Iron mine down in 6-7 turns yeah (can't be more exact, don't know how my builder cost inflated with Currency discovery), right now I'm finishing the second warrior (3 turns). Then builder afterwards (guessing 4 turns should've checked in game

).
Also don't beat yourself up over the missed attack oppertunity. I have a combined 1500+ hours in Civ 5, Civ 6 and the Warlock games (which all share essentially the same movement/combat system) and I still manage to pull some spectacularly

moves all the time.