I have had success with Trizact A30, then cork. It took me a long time to get a uniform finish with cork belts. That's not the cork belts' fault, but my fault for not getting an even enough grind before going to the cork belt. When I first started, it would take me a long time to hand sand a kitchen knife at low grit to get the waviness out. I tried cork belts to reduce hand sanding time but that obviously did not help. As my grinds became more uniform, maybe seven or eight blades into this adventure, I was finally able to get a uniform finish with cork straight off the grinder. At the same time, it did not take much time anymore to hand sand a blade because I could go to 220 or 400 grit straight off the grinder. I spent some time trying to convince myself that a vertical scratch pattern is an acceptable finish on a kitchen knife, but was not entirely successful at that. I think it's not so bad on carbon steel knives as the patina hides the vertical scratch pattern. Recently, I spent a lot of time trying to get a uniform finish with cork belts in the lengthwise direction without success while the Scotchbrite belts works well for this. The Scotchbrite belts seem to have a lot of give and conform to the blade, the cork belts not so much. I like the cork belt finish better, though. It is hard to describe the difference, the Scotchbrite has a texture with longer scratches. They both give a nice satin texture, maybe you could call the cork belt finish "creamier".
Ok, that was a long back story to answer your question "where exactly do cork belts fit into the progression". For me, the answer is unfortunately nowhere. I cannot get a uniform lengthwise texture with them and while I like the surface finish they give me, I cannot bring myself to like a vertical scratch pattern. The progression I am currently using is P60/P120 ceramic, then Trizact A100/A65/A30 on glass and/or felt lined platen. I then use a medium and a super fine Scotchbrite belt in the lengthwise direction with a contact wheel. This gives a pretty nice satin finish, is quick to do and does not involve any hand sanding at all.