Displaying a particular counter number in Running header

I am working on a book that uses section numbers within each chapter and also uses an outline format. For example, in Chapter One, I have:

I. Introduction

A. §1.1 Preliminary Matters

The paragraphs are autonumbered with more than one counter, a letter or number from the outline, along with the section number.

I have a running header at the top of the page. I want this header to display the section number only, but not to display the outline letters.

Right now, my headers look like this: [A. §1.1]

I want my headers instead to look like this: [§1.1]

I also need to use cross references that will display as "§1.1" rather than as "A. 1.1"

Is there a way to create a variable that will omit the first counter and other text and only display the counters I want?