Here's how I understand the four examples (native AmE speaker). Others will probably understand them differently.
The lights are on. John must read his paper.
"Now that the lights are on, John is required to read his paper."
The lights are on. John must be reading his paper.
"Since the lights are on, I infer that John is reading his paper right now."
The lights are on. John would read his paper.
"The lights are on. Ah, back when John was alive, on a typical day he read his paper when the lights were on." (This is a bit of a stretch. Some context is needed to set up the counterfactual situation.)
The lights are on. John would be reading his paper.
"The lights are on. As long as life is progressing in its normal way, John is reading his paper right now."
Will vs. would
To answer your question about whether "will be doing something", if it means an inference or speculation, can always be replaced with "would be doing something", my immediate, gut-level, native speaker's reaction is "No, because 'would' is softer than 'will'."
If that's too vague, here is a clear-cut counterexample:
We think that when the lights come on, John will be reading his paper. If so, that would prove that John was reading in the dark.
Here you really can't replace will be with would be, or you would lose the contrast between the two sentences, which is essential to the meaning. The will be clause states a hypothesis. The would in the following sentence states a consequence of the hypothesis.
I'm not sure if "'would' is softer than 'will'" is helpful to someone learning English, but I think it gives you some idea of how native speakers hear these words and choose between them when a sentence could contain either one. Rules try to capture a lot of specific constructions with these words, but the "softer" idea explains those constructions. For example, "I would like an ice cream sundae" is more polite than "I will have an ice cream sundae" because would comes across as softer than will. "John will be reading his paper" sounds more confident and certain than "John would be reading his paper." A hypothesis is closer to what's known, so it takes will in contrast to a consequence of that hypothesis, which takes would. There must be many more forms that this distinction takes. Sometimes the difference is just a subtle shading, and sometimes it's very clear-cut (like the hypothesis-consequence distinction).
An idea
I like the idea of learning some examples to distinguish these verbs, since examples are ripe for intelligently varying to fit new circumstances, while rules are more rigid and don't prime imagination as well. However, the examples A.1 through A.4 don't seem to work well because they're too far from the "anchoring" senses of the verbs. That makes the meaning of those examples somewhat unclear.
So, maybe it would be most helpful* to memorize some example sentences that are well-known to most native speakers, where the meaning of these verbs is extremely clear and distinct. Knowing these sentences might help a learner hear these verbs and use these verbs in ways that are in sync with most native speakers. Unfortunately, I don't have a list of such sentences off the top of my head. Maybe other people can suggest some.
Footnote
* Notice "would" rather than "will" following "maybe". "Will" could work, too, but it would sound a little pushy. I'm trying to make the suggestion as gently as possible, because it's speculative and I'm really not sure it's going to work, so I chose "would" instead of "will".
Best Answer
I think you could simplify it down to this:
If you need an example of 'will' in the more archaic context, here's one.