Well, it's an interesting question. I searched around some and it seems that should is a variant of would, used to express politeness, whereas shall expresses politeness as well as the future.
From shall v. will:
It is perfectly normal, and somewhat more elegant, to write, for example:
I should be grateful if you would kindly send me your latest catalogue.
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I've never seen a clear "rule" about should or would. How do you know if it's right or wrong to say things like, "I should be grateful if..." or "I would be grateful if..." What's the rule?
It's difficult to give precise rules for words that express so many different emotions.
Both of these examples relate to [should] and [would] in their social [deontic] meanings. Modal verbs have social [deontic] and certainty [epistemic] meanings.
There are strong connections between the two, in fact, the certainty meanings allow us to make sense of modals when we use them to be polite.
If I may refer to a quote from Schoolmarm, I think we can clear this up.
From the same source as above, different authors:
"Should" is used in contexts such as "I should be there on time as I've allowed plenty of leeway in my schedule for disasters", "I should know him, but I can't place his face" and "One should try to write thank you notes immediately upon receipt of gifts."
The first two examples, above, express [should] in a certainty [epistemic] meaning. The meanings intended in your original question don't relate to [should] used this way.
The meanings of [should] and [would], expressed in your examples relate to social [deontic] meanings. They are expressions of politeness, [should] expresses [it's a good thing/the proper thing/the advisable thing to do] as in Schoolmarm's third example.
I've never understood the difference between "should" and "would". Which is correct:
"I should be grateful if..." or
"I would be grateful if..."
Frankly, I would use neither. "I should be grateful" means, to me at least, "I ought to be grateful," as in "I should be grateful. but I'm not." "I would be grateful" suggests to me some kind of conditional statement, as in, "I would be grateful if you had given me $100 ? but you didn't, so I'm not."
Instead, I would use, "I shall be grateful" (formal usage) or "I will be grateful" (informal usage). The distinction between shall and will has been vanishing, but (in formal English) it is still customary to use shall with the first person (I or we) and will with the second and third persons.
From a quiz English for Engineering students
Which of the following sentences is/are more appropriate in style? Why?
A. I would be grateful if you could send me the cheque on 12 January, 2005.
B. I would be grateful if you would send me the cheque on 12 January, 2005.
C. I should be grateful if you would send me the cheque on 12 January, 2005.
(Answer: A and C are more appropriate. B has a stylistic problem because there are two “would” in the sentence and they are used too closely.)
From AskOxford: should
I should be grateful if you would let me know...
From a UK site (Derby) on plain English grammar:
I should be grateful if you would reply by...
I shall be grateful if you will complete the reference.
One more. When I googled the examples, I found both "should be grateful" and "shall be grateful" in the same documents: "I shall be grateful" "i should be grateful" grammar - Google Search
I haven't had time yet to look at their function and distribution. That is, I don't know if speakers are using them interchangeably or not.
Does that help so far?