If you aren't already, one of the best things you can do is record each channel individually into a new track on your DAW so that you have more control over them (EQ/plugins or whatever).
You can do that by muting all of the channels on the Gameboy whilst recording except the one you want to record at that point - off the top of my head I think you press Start + B whilst the cursor is on the relevant channel, then releasing B first. You'll see MUTE on the right hand side with the letter corresponding to the channel that isn't muted missing. That sounds confusing, but it'll make sense when you see it.
Afterwards, line the tracks up to be in synch. There's a few ways to do it. One is to get all channels to make a sort of short kick style sound at the very start of the song that you can easily pick out and use as a reference point to line them up (and later cut out). The way I've been doing it lately is to use an Arduinoboy, and LSDJ in MIDI sync mode so that you can trigger the Gameboy playing from the exact same point in the DAW for each channel.
p.s. Cool tracks! I'm a fan of the stereo panning.
I personally don't like using the keyboard for much else apart from typing words; I was never a big PC gamer either, preferring consoles.