Geographical distribution of "shall"

If you haven't already, you might want to have a look at Mair & Leech's chapter "Current Change in English Sytax" in the Blackwell Handbook of English Linguistics. They give some figures of instances of modals in corpora from the 1960s and 1990s (both UK and US).

Among their conclusions are that there's no corpus evidence that 'shall' has declined specifically in the 1st person; it's simply declined generally, as have all of the 'rare' modals.

I believe the only place there is still a distinction is in the first person plural interrogative.

Shall we is an invitation, and implies that we have some choice about the matter:

Shall we go get ice cream?

Will we is used when we have no say in the matter:

Will we be thrown in jail?

A Concise Grammar of Contemporary English by Randolph Quirk and Sidney Greenbaum says this:

Will for future can be used in all persons throughout the English-speaking world, whereas shall (for 1st person) is largely restricted in this usage to southern British English (§3.37, page 47).

The book is from 1973, so it won't be completely current, but that gives some relatively recent indication.