Just saw this on the Maplin website http://www.maplin.co.uk/low-noise-stereo-preamp-kit-220053 . A lot cheaper than a CMoy and has the right impedances. I could split my 1/8″ jack to DIN cable and put this in the middle with a 9V battery and it could work maybe.

My friend with the tapes also gave me an old stereo audio transformer from RS he said could work. Sounds like some sort of magic bullet, a passive one component solution to clean boosting. I may give it a go but am a bit worried about the arcane stuff about impedance matching and also that I may blow something in the boombox if I’m mistaken about it’s power output.