I wonder whether the secondaries are bifilar? If so, could you unwind the one with higher OCV to meet the other. The load sharing wouldn't be perfect as you would have two slightly different transformers with the same ratio but it would be close and the circulation could be almost eliminated. Clearly if the two secondaries are in different layers that would be more of a faff, as would unwinding the 240V primary to 230V.
I can't help noticing the considerable voltage overhead there, using 15V AC to make 12V DC. Some 40% of the input power (at nominal voltage) is lost in the regulator, which if it is linear is a bit of a nuisance. This adds to the argument that these are not the transformers you are looking for.
Use a high reliability 5A switcher, or even a parallel redundant pair, unless it needs to be linear for noise reasons. I can't remember the last time I powered anything 12V with 50Hz transformers. The only application where I habitually default to linear is analogue audio, but I'm guessing that's not the case here with a single 12V rail. Even some of my custom audio mixers run on switchers.\
I appreciate that in theory its much easier to achieve high MTBF in a simple linear supply than a line-powered switcher, and if you want endurance over 50k hours they look increasingly attractive, but I have tens of thousands of units out there powered 24/7 and failures are rare indeed.