You will want to request Research Letters for both the gun and the barrel Joe. No. 00s were usually ordered in bulk by sporting goods and hardware stores, and the shipping records unfortunately may not document the original purchaser/store. The records should include the purchaser of your 4E, and possibly the original barrel composition.
https://lcsca.clubexpress.com/content.aspx?page_id=22&club_id=43784&module_id=245742