D 1103-1104 feed the -5V 0.3A supply. Since they burn, it could be because the 7905 has shorted. Or maybe one of the smoothing capacitors. Each capacitor should be disconnected, and ohm-checked out of circuit.
You should check the circuitry which runs from the -5V. It's labelled for 0.3A. Can you attach an external 5V supply (inverted to get -5V)? Can you monitor current draw?
There a question whether overmuch current draw would burn the diodes but not the 7905 IC. It would help if you could determine what part gets overheated, but the scope doesn't work at this point.
It might help if you put a low-ohm resistor in the line, at strategic locations, to limit current through that part of the circuit. It might save the diodes during testing of the scope. Try 3 ohm, then 2, then 1. If you're lucky the voltage drop will not be too much.