You have a PM.

The trouble is that the online tool is defaulting to having the first carrier do the ticketing, regardless of whether the first flight is a codeshare or not. IIRC your itinerary is WAW-LHR-LAX, thus putting you at the mercy of BA.

But it dawned on me that you could skip LHR, hence BA, by going WAW-HEL-JFK... which would have AY as the ticketing airline. Or, IIRC IB is now serving WAW, so you could get back to something close to your "original" routing (WAW-LHR-LAX-SJU...) by going WAW-MAD-SJU-LAX... That way IB would be the issuing carrier (hmm) but again, probably wouldn't end up with the big fuel fines.

Also, right now ARN is not a lot more expensive than WAW in USD terms, and has equal or better connections to intercontinental gateways. You might run a dummy test of a DONE3 with ARN-HEL-xxx instead of WAW-LHR-xxx to see if having the ticket issued by AY makes a big difference in cost compared to the BA gouging you mentioned on the web.

One final option to look at in terms of on-line ticketing would be originating in Amman. Jordan is pretty close to the same price as Poland/Sweden, and you could really get a jump on the mileage game by going on the RJ AMM-ORD nonstop as your first flight (using the AA code if you like.) I seem to recall that AA does the ticketing when RJ is the first carrier.

Anyway, if you want to spend a Sunday fooling around with the online tool, I'm betting you can hit a solution that offers some savings, in both dollar and segment terms.