Have you measured the current being supplied by the transformer? If it’s less than 400mA per side and the transformer is still getting hot, maybe you’ve got a faulty transformer?
That layout image looks very nice, what did you use to draw it?
I built a similar PSU and also had this problem. The transformer was getting hot and was also vibrating a bit. My transformer is from Conrad and they have only “2x15 V” transformers, that means it doesn´t have a real center tap but two parallel windings each giving 15 V. The problem disappeared when I changed the wiring to the transformer. You have to choose the right two of the four secondary pins to connect together to the virtual Ground.
I made myself up an explanation - no idea if this is correct: As the windings lie parallel for the whole distance, the electrons have to be “pushed” through the transformer from -15V to +15V in the same direction to not work against each other, so it is essential that you connect the end of one winding to the START of the other one.