Hi Greg. How's Taipei?
Your statement above, where you say that "Would fills the bill rather nicely as a past tense version of shall", isn't an example having anything to do with past tense.
It's merely a past tense FORM being used to denote reported/indirect speech. In the case of modal verbs, it's the HISTORICAL past tense FORM that's used.
The reason that it's so hard to make 'should' act as the past tense of 'shall' is that both verbs are tenseless, in fact, all modal verbs in modern day English are tenseless.
All the modals are used in past, present and future situations so effectively, there are no tensed modals in modern English.