Ill have to stare at the map for awhile, and make up a few attack theories and let Charon counter point them with some marine logic, but I believe your initial assessment serves.
I haven't done an in-depth assessment on the practicality of invading from each faction, by air or land. In fact, we don't even know what type of land force these factions have, or if they even field them outside cities. Oh, and by all means you two take over- I have no ties to military warfare, I merely studied the principles and movements of both World Wars and extrapolated what I learned to here.
Now we have to ask ourselves, from this fictional standpoint, what kind of provisions or alliances have been made that keep the nation independent? Does it act like a geneva or Swedish neutrality?
Has it been so long a neutral state that to violate its territory is considered taboo?
Is its military capability so great that just the act of taking the city would just lead to the mutual destruction of both the city and the enemy attacking army?
In terms of alliances, I assumed it was still there as if anyone moved they would be attacked by another political opponent who had wanted to undermine them for years. However, I don't know for certain, but I drew the nature of their silence due to a sort of Mexican Standoff as opposed to anything else:
The Yeshans are expansionists, they'll want it for the trade route and other points already mentioned. The Arashi League would logically attack as this would significantly reduce the trade flowing through their territory, cutting down the income from raiding.
The Angleans need food, most likely. They're probably paying through the nose to the Yeshans for crops, and being able to produce their own will open up the coffers for an expansion in military which they desperately need. While they have no Third faction to fight, taking the Burren would result in conflict on a North-South front and a East-West front across the Wastes with the Yeshans, and I imagine that in this scenario the Baronies will either make a desperate grab for Anvala now or could perhaps side with the Angleans to rid themselves of the Yeshan threat. However this second option is unlikely as it would ensure Anglean dominance in the area, presenting the Baronies with another problem.
My problem with mapping the Baronies is I don't know their history or the political mindset of the Order of Chaladon:
The Burren may be the ancestral homeland of the Baronies, presenting a reclamation motive as long as financial gains. It is odd how the faction forms in very close proximity yet doesn't utilise or hold the area from the get-go.
On Chaladon, I've compared it to the American isolationist policies of the 1920/30's- if this is the case, and they are on the defensive, using the sea as a wall, then they may not attack the Baronies if they go to war. However, there is no better time to attack them, so they could break isolation* and hit them in the rear. On another note, the area to the South of Chaladon also appears to be contested, suggesting they are perhaps fighting themselves. I'll leave that for another time, as this is long enough as is for one sitting.
Oh, and to raise something else- considering how long it would take to conquer the Burren, surely the other factions would join in the war before the original conflict was completed. This would support you idea that any invasion would cause catastrophic damage. In some ways, I think this war would be too big to happen, but I know logically it is likely due to the nature in which the World Wars started.
*we need to know the effective travel range of an airship fleet before it has to resupply for isolation to be valid.
