You can use a *A Air Pass with a Reward Ticket.
The fare sheet states:
FARES AVAILABLE FOR RESIDENTS OF A
COUNTRY OUTSIDE EUROPE IN CONNEX WITH
TRAVEL TO/VIA EUROPE. THIS FARE MAY ONLY
BE SOLD IN CONJUNCTION WITH AC/BD/CA/FM/
JK/LH/LO/LX/NH/NZ/OS/OZ/SA/SK/SQ/TG/TK/
TP/UA/US/MS INTERCONTINENTAL/
INTERNATIONAL FIRST/BUSINESS AND ECONOMY
CLASS FARE/TICKET/ISSUED OUTSIDE OF
EUROPE FOR TRAVEL IN BOTH DIRECTIONS TO/
FROM EUROPE.
A PASSENGER MAY PURCHASE ONLY ONE STAR
ALLIANCE TICKET FARE PER INTERCONTINENTAL
/INTERNATION JOURNEY.
UPON REQUEST PAX SHALL PRESENT PROOF OF
RESIDENCE. THE AIRPASS MAY BE SOLD IN
COMBINATION WITH REDEMTION/BONUS
PROGRAMME TICKETS.
Options with the airpass would be DUB-CPH-HEL-BCN at US$460+++ or DUB-CPH-HEL-ZRH-MAD at US$580+++.
It isn't a cheap option but may work for you.