However, I am still trying to find the perfect finishing steps for craptastic kitchen knives (of which I sharpen a lot). I know you can't polish a turd, but most of the knives I get to sharpen from other people are these types of knives. It's almost "darned if you do, darned if you don't," whatever stone you choose. Any suggestions highly welcome.
Allow me Sir... to put in yet another shameless plug and other alternative suggestions. Use whatever stone is necessary for repairing/resetting the bevel, then use:
Your Arashiyama 1k to "finish" the edge. Sharpen as usual, then claim some of the mud from this stone with a sheet of paper and carefully wrap it around the dry 6k. Don't saturate it, use just enough water to float the slurry and drag a sheet of paper over the surface of the 1k to collect it. Wrapped around the 6k, the paper should be damp enough to press it nice and flat, but not so wet that its breaking down. You should see the abrasive content coloring the paper. Strop with this to top off the edge - no point in stropping on leather or even with plain paper unless the blade in question is obviously for chopping - the end user will never notice the difference, and the grit from the 1k will work that softer steel nice and easy. If the metal is a real dud, add a bit more water to make the slurry more mobile but try not to overdo it.
I find that method imparts a great edge on this sort of tool, and you're probably using the 1k anyway. I used a diamond sawsall blade to cut 1/4" slice off the end of all my waterstones to use as a perfectly matched Nagura - comes in very handy for generating extra mud when desired or when I wanted to use some slurry but didn't have much grinding to do. A DMT credit card or similar will work too, but it slowly trashed my coarse DMT over time to use it like this (also meaning the DMT was shedding grit into my slurry).
Or you could:
Reset the bevel with appropriate stone and use the black compound with a touch of oil on the washboard. This will give a very nice edge to softer steel, and very little pressure is needed. For those unfortunate enough to not have a Washboard, a sheet of paper wrapped around the coarse side of a combination stone and dosed with black compound will work very well too. A drop of oil worked into the paper allows a bit more mobility to the abrasive and tends to work very well on softer steel. Also a real nice vanilla edge for the average user. Finish on dry plain paper for larger choppers, leave some texture for slicers.
And lastly:
Use 600 grit sandpaper on the Washboard and finish on plain paper, using a bit of pressure to burnish the edge - don't overdo it, softer metal can be worked to a relatively fine edge in this manner and then it will start to burr and degrade along the apex (overhoned). This works well on tougher steel or softer kitchen fare, also a nice middle of the road edge that most users will think plenty sharp.
IMHO the key to doing the softer or cheaper stuff is to not overdo it. It might not take a real fine edge or an overly toothy one for that matter. So middle of the road and done with the understanding the steel is soft and less is more, maybe a nod to the intended usage and spend an extra minute polishing the Chef's knives or obvious choppers - stropping on plain paper or newspaper is usually plenty.
As for the thread topic - edge prep depends on intended use - coarse edge for slicing, fine edge for chopping.