Steve,
That's great news! It appears that the vast majority of the algae is dead, but keep SLAMing until you pass the third test (clear water).
If you keep the pump running and continue to clean the cartridge, the water will eventually clear; however, there are a couple of methods to expedite the process if you are in a big hurry (party planned for this week, etc.). Some of the methods may not be available to you depending on your setup and only the first is condoned by TFP from what I can tell.
1) Brushing pool surfaces daily (or more) - The reason the water looks greyish/white after your brother in law brushes the pool is because he has stirred up all the dead algae (live algae is green, dead algae is grey/white). This allows your filter to clear it out of the pool. Your pool is turning blue again 24 hours after brushing because the dead algae has either been filtered out or settles to the bottom again. With that said, the pool would clear the fastest if you could continually brush it. That it not practical, but brushing often enough to keep it white/milky while you run the pump and filter is optimal. This method has a very high success rate.
2) Flocculant (aka Sink and Sweep) - This is the method most frequently used by pool service companies since the customer is usually complaining about the length of time that it takes to clear the pool and/or the number of service charges. As far as I know, TFP does not recommend this method because it is unnecessary (as long as you have time), wastes water, and because people have a tendency to mess it up. It will not work if you still have live algae in the pool. In order to use flocculant, you must have a pump that can both run in recirculate mode (filter bypass) as well as vacuum to waste. Basically, you brush the pool/stir everything up, add the flocculant and run the pump on recirculate for a few hours. Then, you shut everything down and let the pool sit for 24-48 hours. Almost like magic, the pool will be completely clear after a day or two with a thick layer of dirt and dead algae at the bottom. At that point, the layer of gunk is vacuumed to waste EXTREMELY slowly and the pool is topped off. If at any point in time the flocculant runs through your filter, it will clog and possibly burn out your pump if you leave it running. Despite the fact that it can be difficult to remove the flocculant from the pool once everything settles, this method is the quickest and highly effective if done properly. I've only had to do it twice.
3) Clarifier - A cousin to flocculants, a clarifier will clump small particles together but allow them to stay suspended in the water rather than floating them down to the bottom like flocculant. This allows them to be filtered out more quickly. If you use too much, you will only further cloud the water. Because cartridge filters filter down to about 5 microns anyway, this method has only a moderate success rate for those already using cartridges.
Anyway, keep SLAMing, and good luck. You're on the home stretch! Test results look great!