It really doesn't sound like there is a problem with the output from the miniKorg as you say it is loud through a 120 watt guitar amp. I do think having a mixer would provide the extra gain. The guitar amp's preamp already provides this which is why it seems louder through it.

I don't think you are going to be able to avoid buying an external mixer. Your cheapest option is Behringer mixers that are only around $60. Plus they will provide you with EQ control as well as gain. If you live near a Guitar Center you can always buy one with the option of returning it if it doesn't solve your problem. But I am sure it will.