This one has been burning on my tongue ever since.

Has there ever been any attempt on ripping the background music specifically from
Spider-Man/Spider-Man and his Amazing Friends (1981-1983)?

BGM as in the situational ones.

Never had the chance to get a decent record myself, let alone without fx.

well, found a few here, but there are more
http://www.cartoonopolis.com/music-library/spider-man-music/