Power supply for K2573?

Hello all,
I have a Russian turntable “Elektronika 012”. It works good (after I replaced several Russian electrolytic capacitors) but has only pickup output. I want line out also, so I decided to install the K2573 preamp into it (there’s lot of room).
The turntable has two non-stabilized power sources: +19V and -19V. They are filtered by a 2200 uF capacitor each.
I tried to feed the K2573 thru a 7812 regulator, but there is too much hum. As recommended somewhere in this forum (thank you!), I tried two sequential 9V batteries, and now the hum is considerably lower.
The turntable is quite hard to disassemble, therefore I do not want to continue using the batteries.
Any recommendations how I could get usable power from the two 19V sources? Thank you in advance!

If a regulator does not do the job, then I’m afraid you will have to stick to batteries.
Of course, we have to assume that the voltage regulator is doing its job correctly and that the wiring has been performed according to the rules of good engineering, to avoid e.g. hum loop, etc…