I'm assuming the 2nd pin down on the transformer connects to R8 and R13, so something from the LNK623-626
LinkSwitch-CV Family should be suitable.
My main experience is having replaced hundreds of blown LNK624DG on washer controller boards for the last 10 years. I soon discovered that using the LNK626DG as a replacement greatly improved reliability.
The higher numbered variants have higher peak current so there is some risk of transformer saturation but never occurred in my situation.
Also, a small percentage of transformers get damaged by the high current surge during the blow-up. I can pick them by checking primary resistance as it is already known to me.