Can I replace a power transformer inside a device with a DC jack and external power supply?
Apart from the capacitors, the problem could also be caused by a faulty diode D 503 or faulty transistor TR 511.

Since you have already replaced the capacitors, you may go ahead and check the diodes and the transistor.
The transistor is part of a 'capacitance multiplier' circuit. It multiplies the capacitance value of C 526 by the factor 'β' (current gain of the transistor).
It would be worth your while, should you be able to maintain the originality of the unit.