Is that this one? GitHub - twinturbo/KOSMOPSU: This is a KICAD PCB Design to build a mains to +12V -12V Power supply for analogue synthesizers I guess you’ve had that a year or so now, any issues? I might look into building something based on that.
Not sure the beefiness of the transformer is the relevant thing, though. Would undersupplying the PSU cause a regulator to shut down? I don’t know, maybe. But one other thing I see there is you have only 1000 µF on each rail. There was some discussion of that here with @feralbeagle saying the 10,000 µF or more of the MFOS or FC wall wart supply was too large (bad for the diodes) and suggesting 3300 µF. And you went even lower.
The other difference is your transformer is center tapped, and you have a full wave rectifier. There again I don’t know if that’s relevant but it is a point of difference.
By the way, I spotted an issue on your PCB:
No connection across the power header for the -12V rail.