Third photo is hard to say but I think, like on second and third photo is layer of paint, grey paint from outside, do you think this is possible?
That was the photo that I was referring to as less successful than the rest. But now I understand it may be for other reasons. Unfortunately it may not be possible to clean everything perfectly, just the nature of these things I guess. But more important is overall you have got most of the inside of the block very clean with a good job and it will be fine.
When I flush after the acid, it is first with only water, running for awhile through the system (like water flowing from a garden hose). That is to rinse out as much acid as possible. Then I mix the soda in clean water (like in a bucket) and fill the system. Let that soak for a while to neutralize any remaining acid. Then if it looks like much soda settled and dried inside, I will flush again with just water (same like before with the hose). So no matter how you do it there will be water remaining inside. No way to avoid that. If you can dry out all of that water then there will be less rust (like comparing your first and second photos). But it may be difficult to get all of the water out, so some light rust may form (like the second photo). I think it is the best than can be done, and not enough to be any problems. Most important is it is much better than before.
It will be interesting to see what you get with using phosphoric acid next. But it is not necessary in my opinion, I think what you now have is good. If you have some and decide to try, I will be interested to see photos to compare with the current ones. I have not done this to a block, but with many other parts so I am following your project.
Another good cleaning chemical for cooling systems is Oxalic acid. It is very mild and more for a complete cooling system "flush" to generally clean it (great for radiators). It will not remove the heavy scale but will get rid of most rust and normal accumulation. Many of the good cooling system flush products in the past were Oxalic acid, until our government decided it should not be dumped on the ground so stopped it. But you can still get plain Oxalic acid and make your own flush. It comes as a powder that is mixed in water and run through the system for about an hour. Then rinsed with water, and finally neutralized with soda mix (mosty to protect soft materials like hoses). But if are starting with everything new (clean block, new radiator, etc), then this isn't necessary.
Regarding oil squirters. I would like to hear more about what you can do for a retrofit. Feel free to contact me by email (same address as before) or by message here. Thanks.