I would use... (gulp) ...semiconductors:
You can power one dual opamp from the 12V filament supply, but naturally you must implement some rectifying and filtering to turn AC into DC. Make one half of that dual opamp a unity gain, non-inverting buffer, the other half an inverting unity gain amp. Now you have both balanced outputs and a low output Z "buffered" output that isn't too picky on what you connect this preamp to.
e.g.
The schematic is just an illustration of the concept. Do note proper biasing and coupling required by unipolar supply! For extra safety wire back-to-back diodes from each output to Vcc and COM.
That original preamp design has way too excessive output impedance, which also varies in interaction with tone control dials. It expects to see a very high input impedance in order to not color the tone or attenuate the signal too much. Unfortunately, while most -guitar amp- preamp input stages fulfill that clause about high input impedance most power amp input stages (to which you'd be connecting this unit) will not. Even less other devices... In a computer interface expect maybe around 10K input impedance. That's much, much less than the common 1M of guitar preamps. Therefore you practically need to buffer that output.