New Grand Company (Side)Quests

For the following three quests...

It's a Piece of Cake to Bake a Poison Cake
Woes of the Botanist
A Weaver and a Mummer

...what are the requirements to start them? As an Adder, Sergeant First Class, I was only able to pick up Woes of the Botanist. Any chance that the other two unlock for Adders at Chief Sergeant? Or are each of these three quests unique to the members of their local grand company, unlike the three Beastmen Stronghold quests that were introduced last patch?

Flame Sergeant First Class

Was able to pick up "A Weaver and a Mummer" (complete)
Unable to pick up the other 2...

(WVR@45, BOT@29, CUL@0)

Hope that helps.

I think you can only pick up the one in the town of your GC. I was able to get the Cake one, but not the others as a Maelstrom member.

Correct, you can only pick up the one associated with your GC.