Is my sea star doomed?

Honestly I don't know the quantity of water. I put him & bag water in a 5 gallon bucket and set up the drip at about 1/sec. Every so often I would remove a cup of the bucket water to get the tank to bag ratio to increase.

 

your drip rate is fine, perhaps even a touch slower than I drip (probably closer to 2-3/sec) I like to fill the 5 gallon pale ensuring that the water in the pale is more or less identicle to my tank. I also cover the pale with a box so no one gets stressed - then I kill the tank lights before adding them to the tank.

Again, it sounds like you did it all right.

 

UPDATE: Still alive, though the same little puff ball looking thing is now on a third leg.

-AJ