There are two things that stand out to me. The first is 12 gallons of 1.061 needs at least a 5 liter starter. So you pitch about 1/5 the required liquid yeast. I know you used dry yeast. Still 17.25g short of ideal dry yeast pitch.
The second is you pitched 11.5 grams of yeast into a 1 liter starter. There is not enough sugar in a 1 liter starter to force a growth phase from that amount of yeast.
Yeast can be trained. If you talk to professional brewers, they think the best beer comes from the fourth or fifth batches of beer on the same yeast. Because they have trained the yeast to do what they want. You way over pitched your starter hoping to get it the yeast active. What you trained them to do is shorten the growth phase because there is not enough sugar to feed all of them. Then you way underpitch your beer. The yeast repeat the shortened growth phase and the realize there's way more sugar then they can handle alone! By then it's to late they have already started producing CO2 and alcohol. Now the environment is still rich in sugars but toxic. So the yeast army depleted before they could finish the mission.
When I make a big starter, I start the starter 3-4 days before my brew day. I put it on my stirplate for about 12-18 hours. Then I let it sit until my brew day. On brew day I move it to my fermentation chamber and start get it acclimated to the temperature. By the time I'm ready to pitch all of the yeast is in a nice cake at the bottom. I decant almost all of the spent starter wort off the top. Leaving just the yeast cake and enough beer to mix it up into a slurry.
Oxygen is key for a growth phase in Yeast. I would oxygenate your starter. Not sure that swishing it around is enough. I guess you could shake the hell out of it. But 10 seconds of pure O2 or a stirplate would surely grow more yeast.