According to your Lodestone page you're a First Lieutenant in the Maelstrom so you should be able to access the Hunt Board at Maelstrom HQ in Limsa Lominsa with no problems.

I assume as you said you're now a 2nd Serpent Lieutenant though the Lodestone page is probably outdated, but have you tried speaking to the Allied Quartermaster at Twin Adder HQ nearby? (The soldier in the garish yellow robe near the entrance who is a vendor for the Hunt). I've never changed GC alliegance so I have no idea how that affects the Hunt I'm sorry.