Hi JF and Owner,
In my call to BAPI_OUTB_DELIVERY_CHANGE, I was able to update the partner address details by using the BAPI's header_partner and header_partner_addr parameters. I populated these parameters as follows...
data ls_partner type bapidlvpartnerchg. data ls_partner_addr type bapidlvpartnaddrchg. ls_partner-upd_mode_partn = 'U'. " update partner ls_partner-deliv_numb = delivery_number. ls_partner-partn_role = partner_role. ls_partner-partner_no = customer_number. ls_partner-address_no = address_number. case abap_true. when use_customer_address. " i.e., address_number is the customer's KNA1-ADRNR address number ls_partner-manual_addr = abap_false. when others. " manual address ls_partner-manual_addr = abap_true. ls_partner_addr-upd_mode_adr = 'U'. " create or update address ls_partner_addr-addr_no = address_number. ls_partner_addr-name = name1. ls_partner_addr-name_2 = name2. ls_partner_addr-city = city. ls_partner_addr-postl_cod1 = postal_code. ls_partner_addr-street = street. ls_partner_addr-str_suppl2 = street_suppl2. ls_partner_addr-location = location. ls_partner_addr-country = country. ls_partner_addr-region = region. ls_partner_addr-tel1_numbr = telephone_number. append ls_partner_addr to header_partner_addr. endcase. append ls_partner to header_partner.
Good luck. 
Amy