Actually, I'm going to make a suggestion: we should entirely ignore the naval side.
Now, I know you're going to think I'm bonkers, so let me expand.
1) We don't really need a navy that much.
What is a navy good for? Protect your trade and attack the enemy's, project your land force and keep communication and supply channel open to your oversea possessions. We don't have trade or oversea possessions, and we have an enemy right at hand so we don't need to project your force.
In game terms, a navy would let us attack the Brits and maybe gain a point or two of logistic. But we don't need to attack the Brits, and we can get logistic by other mean (also, I'd guess that sea-based logistic would be susceptible to enemy raiders in a way that a train would not.)
Another benefit would be to prevent the Brits from attacking us, but even if they have total sea superiority, it is going to be impossible for them to make inroad if we focus on land warfare. We can just push them back into the sea.
2) We are unlikely to win the naval game
Unlike us, the loyalists NEED to win on the sea to be able to do anything. That means that they will spend as much design and revision phase as they need to get naval superiority. And since many of those were on my side in the Arstotzka game, I know they have good designers.
So we're facing an enemy willing to throw everything in the naval arms race. But we don't have that luxury, because we are also facing a land enemy.
3) We need to get the Loyalists and Monarchy to fight each other.
There is a good reason Zanze banned any diplomacy. If two sides managed to gang on the third, they're pretty sure to win. However, it's still in our interest to get the Monarchy and Loyalists to fight each others as much as possible. So I say, let us stay out of the naval game, and let them keep fighting on the seas while we take over the Monarchy. We can then crush the loyalists with a continent's worth of ressources.