I actually think we should move our chariot to the forested square across the river from the barb city. This seems to be a gamble with limited risk but a very large payoff.
Here is the plan.
1) We advance the chariot 1 square along the river, checking if there are axes in those forests. If there are axes, we go across the river and kill the weak axe. This checking move has no risk to us because according to the latest screen, we cannot reach that 3.9 axe on the forested hill across the river from us.
2) If there no axes in the forests, we advance onto the forest across the river from the barb city. The question is, will there be axes in the forests beyond? We don't know, but we know Sancta had units on the way from somewhere. But the chances of there being units in precisely those squares is well less than 100%. So maybe say 50%--and that's a really high guess. That weak axe across the river is no threat to us.
3) if there are indeed axes, what are the chances that they kill our chariot? Again, it's less than 100%. I think the winning pct of a 1 combat axe vs a 1 combat chariot is about 70-75%. So in conclusion, what are the chances of there being an axe next to us AND we die? It obviously depends on the chances of there being axes nearby. If we assume 50%, we are talking about an "adverse" scenario of maybe 35-40%.
The benefits obviously are large. We would be in a position of razing the city if it's tactically possible, and we would unveil a few more squares and maybe spot any nearby Sancta units. We can also further advance to the forest hill beyond if we want to the turn after. We can also check out the garrison inside the barb city.
If that doesn't work out (i.e. the garrison is too large and our chances of razing the city are nil), we are still in a good position to strike at the injured Sancta axes in 1-2 additional turns, depending on where they move.
So, it just seems to me that moving to the forest across the river from the barb city is a low risk, very high reward proposition.
What we really give up is the ability for the injured axes to heal 1 turn. So that translates into 0.5 health per axe... But a full health chariot vs a 2.1 health axe = no contest. I'd guess the incremental HP's lost by us is small because our chariot has an effective attack power of over 8.