Egads, you are a brave soul. If that was a powered headphone output you could have smoked your laptop. Well, maybe, maybe not. See http://www.sweetwater.com/expert-center/techtips/d--10/26/2000
There may be a headphone to line level converter somewhere, you'd have to do a bit of research to find one though. Personally, I would recommend a good microphone.
Remember your line in is probably stereo, so make sure you are using the right converter jacks. That and the impedance from headphone to line level is a bit different, and figuring it out from an organ that old is probably hard unless someone has a service manual. I know enough about electronics to be dangerous and fix most of my own stuff, but the albeit-simple-if-you-understand-it math for matching impedance (ohms resistance) and voltage escapes me, even though I took Calculus in high school. You should be able to turn down the input on your computer far enough where you are not clipping the signal using what you have now, but if there is any interference on the line then you need a better cable. You can probably use a shielded cable if you needed to, but the shield (you technically have THREE wires with a shielded cable) would be what you use for ground, not the headphone out ground. The problem with what you are doing is that you don't know what is being grounded from your ground lug on your organ, which I'm surprised has a ground, I don't think they had 3 prong plugs in general use in 1971. It almost sounds like you are using the neutral line, which eventually connects to ground at the breaker box, but is definitely not a ground per se.