Fascinating. As a native northern-US speaker, I literally had no idea how these used to work until now. (I guess most people know this, but here the sense you mentioned is the only one acceptable in speech; otherwise, "shall" sounds more commanding than "will" but archaic; and "should" always means "ought to".)

As a native German speaker, the way I understand it is (generally):

sollen = shall

sollten = should

werden = will

würden = would

i.e.

Werden wir gehen? = Will we go?

Sollen wir gehen? = Shall we go?

Sollten wir gehen? = Should we go?

Würden wir gehen? = Would we go?

At least Google Translate seems to agree with me (although of course it recommends "Are we going to go?" for the first one).

In other words:

"Would" is speculative but about behaviour: "If this happened, would we do that?" (i.e. does this accurately describe our behaviour?) "I wouldn't do that if I were you..." (you aren't going to see me engage in that kind of behaviour and it's probably a good idea to follow my example)

"Should" is speculative but about obligations: "If this happened, should we do that?" (i.e. are we morally obliged to do that?, or: is it a good idea to do that?) "I shouldn't eat this cake..." (I may or may not eat the cake, but I know it's not a good idea to do so)

"Will" is also about the future but fairly objective: "When this happens, will we do that?" (Yes/No/Maybe) "I will not buy this record, it is scratched!" (Me buying this record isn't going to happen and there is no reason to doubt this prediction)

"Shall" is about an imminent decision: "Now that this has happened, shall we do that?" (Yes/No/Maybe) / "I shall eat this cake!" (I have decided to eat this cake and wish to inform you about my intent)

Of course those rules of thumb aren't entirely foolproof.

"Thou shalt not kill" (or "You shall not kill") is different because it is a command. It makes the decision for you. If it were "you should not kill", it still leaves it up to you to actually follow through on that command.

I'm not entirely sure about Fowler's description of "I will" as "it is my will to". This seems to contradict the equivalent usage of "ich werde" in German (where "ich will" actually means "I want", merely declaring a desire -- e.g. "I want a pony" doesn't mean you are intent on acquiring a pony it just means you'd really prefer having a pony over your present state of pony-non-ownership).

EDIT: Also note that in German "werde" can also mean "to become" (and "bekomme" means "receive", leading to the common mixup "I become a hamburger" at fast food parlors). Going by that meaning "I will kill you" could also be read as "I {am most certainly going to become} {a person who kills} you"). There's probably a clever observation of the usage of nouns and verbs here for a proper linguist.