Update: I have tried vac-ing to filter per @Watermom's suggestion in #27. Didn't seem to help and now I'm also noticing sand residue in the hose after I backwash. Here are the details:

First, I left my pump off for about 13 hours. After that, the pool had cleared SOME although it was still a little cloudy.

Then, I started the vac process.

To be clear, since I got confused about this yesterday, I was set to FILTER on my sand tank. I went V-E-R-Y S-L-O-W-L-Y. I tried to take my time to make sure that I wasn't stirring stuff up before it could get into the filtration system. I also tried to work my way around the pool so that - as I progressed - I only stepped on areas that had already been vacuumed.

There was DEFINITELY a thin layer of something on the pool floor, all across the floor. In addition, large clusters of brown-ish "gunk" had settled in various pool crevices. I slowly passed my vac over all this stuff, and it vanished.

HOWEVER, there was a problem. After I got a little way into the process, I noticed that the pool was definitely becoming a little cloudier around the return inlet on the pool. The area where I was vacuuming seemed okay, but the return area was definitely a little murkier. I didn't take this at a good sign, but I nevertheless finished vac-ing the entire pool floor. I covered every square inch of the pool floor using the technique I described above. Once I was done the pool was a less clear than it was before I started. Its all a very nice shade of blue - its just murky.

Then, I backwashed, just to see if I had caught anything. Sure enough, once the backwash started I got a stream of white, but extremely cloudy water. It even looked cloudy sitting on the ground in pools. I would describe it as milky-white. Eventually, the backwash stream cleared. I then rinsed and restarted the filter.

Thereafter, I discovered a NEW problem. When I disconnected the backwash hose, I noticed a ring of sand (zeo?) around the valve where I connect the hose. I also noticed a little sand sticking to the inside of the area of the hose where it was connected to the backwash valve. Didn't notice it anywhere else in the hose (e.g., none at the other end of the hose and didn't feel any sand in the hose as I was rolling it up.) I've never noticed this before, and I think I would remember it if it had happened.

Now that I'm sure I'm free of algae, I'm pretty sure the pool has a lot of fine particles that are just getting through the filtration system. Here are the options I'm considering, though I'm open to others:

1. Try the "DE" test by putting a cup or two of DE in my filter to see if it comes out the inlet.
2. Putting enough DE in the fliter to "help" the zeo in my tank get the smaller items.
3. Filter sock. (Anyone had luck dealing with a problem like this using a sock?)
4. Floc and vacuum. However, I'm worried about whether I won't end up with the same problem, even after flocing.
5. Let everything settle REALLY well and vacuum the floor to waste. This will be a LONG process. I'll have to stop after 10 mins of vac-ing to get the water level back up to the skimmer (which will take about 30 minutes). It will definitely be a Saturday afternoon project.
6. Honestly, it would be just as easy as #5 to just drain the pool down to about 18" and then re-fill.

I'd really like more options. Can anyone think of any?