Kim makes a good point. So for any curious pool owner who finds this thread some day in the future.... You can't just toss in the flock and cross your fingers. You really need to have patience and plan. Here's how it's working out for me.

Late Wednesday Afternoon - Made a slurry with the Alum in a bucket. Stirred it up with a big piece of PVC pipe. Stirred. Stirred. Stirred a little bit more. Set valve to recirculate. Removed skimmer basket. Then I cast/splashed the slurry mix evenly around the pool. Let the pump run for two hours. Then cut it off and went to bed.

Early Thursday Morning - Woke up and was stunned by the increase in clarity. You can see the Alum "goo" on the bottom, it looks almost like a reflection of the clouds.
Late Thursday Evening - Got home late from work. It was nearly dark. The layer of Alum goo had increased significantly. I hooked up the vacuum, turned off suction from my main drain so only the skimmer (where my vac hooks up) was sucking,
set valve to waste, <--VERY IMPORTANT, turned on the water hose so I could offset the water loss from vacuuming to waste, and finally kicked on the pump. Vacuuming the goo feels almost like you're vacuuming up fog or a cloud. If you go too fast, or if you're too aggressive with your movements you'll stir up the cloud. It took me about three cycles of vacuuming until water levels dropped to near the bottom of the skimmer then stopping to let water levels rise, repeat. Here's how it looked when I was finished.
Friday - I decided to let the water sit still today just in case there was still some floc in the water column that needed to drop. I'll vac again this evening, add a sock to the skimmer basket and keep an eye on this while filtering and back washing as needed.
Sorry for the crummy picture quality. My phone's primary camera is broken so I have to take everything with the selfie camera!
All said and done, I think over the past two weeks I've added 14 jugs of 128 .oz 10% bleach. The first few days, I went through chlorine like candy.... The next several days were down to about a jug a day.... And this past week has been about half a jug a day. I assume I would've needed at least another two weeks and 8 more jugs to get to the finish line.
So... While Alum is not for everyone and is essentially treating the symptoms not the cause... I think with patience and research, it can be a helpful tool to be aware of.