Those all sound like good ideas, whatever works, right. Here's what I do. I take it out of the lye water, rinse with cold water to get the lye water off, then I let the piece/pieces soak in dawn detergent water overnight.
The next day you pick the piece up, and all that black slime, you wipe that off with paper towels and then go over the piece good with an SOS pad, then rinse it off with cold water, dry it off good, and then put it in the oven and let it good and hot for an hour or so at 400 degrees, then I take it out and put mineral oil on it, it smokes just a tad at 400 degrees, and I put the mineral oil on with a brush, it goes on very nice and even and complete when its hot like that, then I let it cool and wipe it off with a tee shirt, fruit of the loom, and then I can display it, the mineral oil darkens it, and it looks good.
Now if I was going to season it, after I washed it off with the SOS pad, and rinsed it off with cold water, then I would season it.