The gravy is great, but influence seems a little funky.
Being apart of the navy appears to give no benifits when it comes to influece.
we also get no infamy from islands
so what if we did navy activities:
Protect locals from a raid
give a speech
recruit members (castaways likely by bringing them to silverhold or other navy bases)
by doing these activities maybe we could get more influence OR these activities would be ordered based on severity.
how does this help players in the navy though, well we would get some rewards but also maybe at low infamy the harder quests like defend a town would give more rewards.
this seems like a better way to immerse the navy into the world