Just because the water came out clear, does not mean it dissolved and flushed out all the old, hardened gunk. Can you see straight down from your toilet into this tank? Turn water off, open flush valve in toilet, and look down with a flashlight. If you can see the bottom, it might tell you what is there. Also, try using a metal rod of some sort to stir stuff up if you can.
Also, my trick was to fill tank about 1/3 full and find an isolated road where i can swerve, stop hard, accelerate hard briefly, etc. (Road needs to be isolated so people will not think you are nuts or drunk.) In other words, you are stirring the tank via your driving. THEN, try dumping it again and see if more stuff comes out.