I'd go with AA namely bc of price, then QR, then AY. You should have excellent lounges in DOH/HEL on your layover, but many people just want to get to their destination ASAP. The nice thing about AY is you have the 330/350 on both routes which is a bit wider than the 777 that AA offers. QR has both depending on the departure flight.

Not sure why you think you'd have a mediocre lounge experience on QR/AY - both give you access to Soho as EXP, HEL has a fairly nice spread at HEL (including showers, good drinks including a couple champers + liquors, and the sauna area). DOH gives platinum lounge access, which while it's no AM/AS, it's still a very nice lounge in its own right with champagne (same ones as AM/AS), a la carte menu, showers, and a rest area. I like to say that most of the complainers would stop complaining if the Platinum lounge was exactly the same but was also the main J/F lounges in place of AM/AS. In other words, people have FOMO.