I will continue to fly them going to Asia, especially with the A350s now coming in.
First, I had four flights with them now (mostly on the HEL-SIN route) operated by A340s where they sell the rear business class cabin as economy and put elites (yes, not only AY+ members but even oneworld status customers!) in those seats. You get economy service with the business seat, but I couldn't care less.
Second, op-ups happen more often than with other airlines. AY seems to (successfully - flights are full even in the dead of winter) cater to the low-end leisure market and apparently oversells/overbooks the Y cabin especially on the Thailand flights with recurring regularity. Result: status customers, even OW ones like me, get a free ride in J. No complaints.
Third - they started to monetize excess J capacity by selling cheap upgrades to J (EUR 350 one way on the routes I fly) online in advance. A typical discount economy 600 EUR ticket plus a 700 EUR upgrade would put me in a J seat for way less money than I'd have to shell out even for MH or the ME3 promo prices.

Last but not least, if I have to fly economy, their 'economy comfort' product offers the most legroom of any competing airline. Economy comfort is a new thing they just rolled out last month - the first few rows of Y on their longhaul flights feature 36 inches of pitch, fancy headrests, a basic amenity kit and semi-decent Sennheiser noise-cancelling headphones. I'd really recommend buying up to this for anyone without status - oneworld sapphire and emerald status holders get it for free, but the price is more than fair at just 60 Euros extra.

Staying on topic here:
Did anyone here take them up on these 350 Euro upgrade offers, and what was the effect on earning mileage in AAdvantage?
I have no idea if they reissue the ticket and what fare class these upgrades book into. Would be great if anyone could shed some light on this!