Anyway, designs.
Don't kill me if this goes wrong, but I don't think we need to design new naval forces at this time. Our navy crushed the enemy fleet despite being outnumbered 2:1 (where they got that many ships from, I have no idea), losing only one of our ships (the Nelson, sadly) while taking out 5 enemy ships, as well as the brunt of the invasion forces. In addition to that, our naval forces will be reinforced by our newest Cutters. We had them last turn, and now that the shipyard is build we can deploy them. I'm willing to spend both a focus and the production focus on the seas though.
Our artillery appears to be sufficient (if we take into account the gun stolen from the Monarchy), and our infantry gun can probably be fixed with a revision, if we want to spend any more time on it. I don't think we should develop Grenades. Grenadiers were an elite force because they were made of people brave and strong enough to throw heavy metal spheres at the enemy from the front of the line, not because the grenades were particularly effective. In addition the increasing range of our weaponry pretty much ensures that grenades are rapidly becoming more obsolete, until of course the development of trench warfare, where the range of engagement again greatly diminished.
Our primary problem that caused us to fail the invasion appears to have been the enemy cavalry. Now, having a better infantry gun would do great for that, so I think a revision can resolve that.
Proposal :
Industrial Steam Turbine : A system of powerfull steam turbines, intended to improve domestic production of resources and gather valuable expertise to implement in later technologies, such as ships.
@Khashykk : You also forgot to add our freshly stolen Pirate cutter to our design list.