The maximum safe current would be the same as the dot matrix controller board fuse: 3/8 amp. Is there more headroom available from that winding on the WPC transformer? Probably a bit, but probably not much. Do you want to risk nuking your hard-to-replace WPC transformer for the sake of saving a bit of extra wiring?
The safest way would be to tap off the line voltage feeds coming from the power junction box that lead to the transformer voltage select plug, and either hard-wire a small power supply for the LED panel/controller or install a small service outlet and plug the LED panel/controller into that outlet.