What I was thinking was not to dissolve them (they won't, it's too much salt and not enough water), but to just let them settle down on the bottom of the vial. Therefore, you would have a near saturated solution in the container, which is just slowly diluted by tank water.
I imagine you could use bigger vials for KNO3 and K2SO4, and thinner ones for KH2PO4. Say you use 5 tsp of KNO3 for 2 weeks of dosing, you'd fill a thicker glass half of that, fill with water, let it settle, plug it shut and attach with rubber sucker in tank. Say you use 1/2 tsp of KH2PO4, you find a really thin vial, and do the same. Size of the diffusion hole would be the main regulation mechanism.
Now this sounds very workable! When the vial shows no solids in it would be the time to replenish it. One possible problem, which may account for what you saw after one day: water with varying amounts of salts in it will stratify and be pretty stable. I think there needs to be some slight stirring going on, or I'm not sure if there would be any diffusion going on at all. At least this is easily testable, as you are doing. A person with a fresh mind for doing the calculations necessary should be able to find out theoretically how fast the "salty" water would diffuse out.