If you can't get to the wire edge on the back of the chisel, you have a problem. some old ones are in such bad shape that you can get to it on part of the edge, but the rest is relieved. You're left working that wire edge off with compound or something in order to get rid of it (leaving it on and calling it good enough is a "fail" effort unless you're working on rustic pine barn doors and butchering them on purpose).
I can't tell from the OP's first picture if he could get to the wire edge, but if he could, I'd have started working with that and let time and edge refreshing work the back to its final flatness.
Unlike Jacob, I flatten everything first to make sure I can get to the wire edge. I don't spend gobs of time working up to a bright polish then, the first bit of use will leave scratches up the back side of the chisel (cosmetic in nature) and are you going to then waste your time every time you sharpen trying to get superficial stuff like that out? I hope not. You can if you use a medium stone like a washita, it'll take those right out, but if you use a slow 1 micron synthetic stone, you're peeing into the breeze.
Once I get basic flatness, I stop preparing a chisel, though - it'll take a few sharpening cycles to polish the back, but it's a whole lot more fun doing that than it is rubbing chisels on abrasive for an hour.
https://www.youtube.com/watch?v=Z7iYFusg0Tc&t=953s
At the point where a washita can reach the wire edge, the surface planed will be bright even if it's not perfectly clear of any plane marks at all (that only matters if you finish plane). The chisels above easily shave arm hair - anything does if the wire edge has been completely removed - even an india stone will do that, but the earlier you stop, the more you have to do to remove the wire edge.
A run of PSA sandpaper roll stuck to glass is by far the best way to conquer anything that's not ready to go right off of a medium stone. The same about effort is true - get it basically flat so that you can get to the wire edge, and then you will gradually polish the back over time just in use, but you can get functionally sharp right away without doing more than a minute or two of work to knock the smartness out of the coarsely sanded edge that a long lap leaves.
FWIW, I prepared a set of 10 neglected japanese chisels two weeks ago in about half an hour, and that included a significant amount of CBN grinding and some very heavy back removal to take the belly out of the chisels. I'd have never gotten them done if i'd have used stones instead to do all of the back side work. A belt sander is out of the question (something always gets rounded because the belt can't stay completely tight).