Yeah, there are numerous techniques you can try. The thing about modern recording equipment like your Zoom device is they try to record at the highest possible quality obviously. However, you can achieve sounds like this through recording techniques and simple EQing. If you were recording with normal mic's and a mixer you could try to increase the gain on the microphones which would cause the vocals and instruments to come out as they did in that recording, albeit they are clipping they were re-normalized to a listenable sound level. I have Adobe Audition which is great for lowering the noise floor for high quality recordings, but it also has some equalizer presets that emulate mid 60's mixers and there is one preset that is called "Lo-Fi". I will try it, and if it comes out great, I can give you the boosts and cuts for each hz rating so you can try it to your already recorded stuff in a free program, like Audacity.
