Where on the timeline is our server?

Margaery_Tyrell

Shadowbinder
I doubt Paxter has started working on King Joffreys Valor as they remained neutral during the Reach’s siding with Renly (the Redwyne Twins were hostages of the Lannisters) and only sided with Joffrey when the Tyrells did.

Doesn't make much sense unless Paxter was going to betray the Tyrells, the rest of the Reach and Renly for Joffrey which all indication points to it being unlikely.
 

Gealrüable

Emissary
construction could have started before all this though, without any political agenda behind it. Perhaps it was originally started for Robert?
I dont know the exact quotes from the books tho, so this might not fit.
 

EStoop

Steward of Oldtown, Knight of Fairmarket
With an active war going on I'd be surprised if the arsenal wasn't popping out warships at maximum efficiency already, regardless wether they are currently neutral or actively involved in it.

Even if the ship was already under construction, I doubt much would point towards it being Joffrey's Valor.
 

Azulejo

Aeromancer
Then it was time for gifts. It was traditional in the Reach to give presents to bride and groom on the morning of their wedding; on the morrow they would receive more presents as a couple, but today's tokens were for their separate persons.
From Jalabhar Xho, Joffrey received a great bow of golden wood and quiver of long arrows fletched with green and scarlet feathers; from Lady Tanda a pair of supple riding boots; from Ser Kevan a magnificent red leather jousting saddle; a red gold brooch wrought in the shape of a scorpion from the Dornishman, Prince Oberyn; silver spurs from Ser Addam Marbrand; a red silk tourney pavilion from Lord Mathis Rowan. Lord Paxter Redwyne brought forth a beautiful wooden model of the war galley of two hundred oars being built even now on the Arbor. "If it please Your Grace, she will be called King Joffrey's Valor," he said, and Joff allowed that he was very pleased indeed. "I will make it my flagship when I sail to Dragonstone to kill my traitor uncle Stannis," he said.​
The galley is a present from the Redwynes to Joffrey the day of the wedding. It is not something ordered by Joffrey, but a way of the Arbor to show support to the new king. Since in our timeline the Reach supports Renly, I think it's safe to assume that the galley is not being built. The ship is probably on the very early stages of construction at that time.

There's a chance that the galley was ordered by someone at the Red Keep and Joffrey only knows about it the day of the wedding, when it is presented to him as a gift from the Reach. Even then I doubt that the Arbor would've responded to a shipbuilding request of the Red Keep at the time our server is set. They are, as Marge said, in opposing sides.​