Let's go with the poodles thought experiment. The principle of flotation says that an object afloat will displace a volume of liquid with weight equal to the weight of the object. Note that it is only the liquid displaced by the floating object that matters, not the average density of the contents of the container. If you have rocks or flocculated yeast at the bottom of your container they will affect the weight-to-volume ratio of the container as a whole but if the float does not go low enough to touch the rocks or yeast, then only the density of the liquid on top matters.
Now to the poodles. If you have a bunch of normal-sized poodles in a swimming pool and you drop a normal-sized hydrometer float in between them, your reading will be the same as if the poodles aren't there because they aren't being displaced significantly by your float. If you drop your float right on top of a poodle it will not sink at all, and your reading will be grossly affected (giving a very high density reading). Now imagine the poodle getting smaller and smaller until the weight of the float is comparable to the weight of the poodle. Now the extra weight on top of the poodle will begin to push it down in the water and your float will sink a bit, giving intermediate readings. Now imagine that you have billions of microscopic poodles per liter of water and you drop your float on top of them. It will displace many poodles along with the water, and give a reading that reflects the density of (poodle weight in displaced volume + water weight in displaced volume)/displaced volume. Assuming that the poodles are denser than water (my experience is that some poodles are denser than others) then the density reading will go up as more poodles are added per liter. That is the case for yeast. For real microscopic poodles (??), which were assumed to be floating at the start, their density is less than water so a lower reading would be obtained.
Jim's experiment is consistent with this. When he had flour particles in suspension, they were displaced by his float and raised the reading. After the all sank to the bottom they were no longer displaced by his float and his reading was back to that of water.