As the title says I am looking for some method of having two instances of the same Java application (that lack this type of setting) to access the internet using different adapters.
I found a couple of questions regarding the topic, here, but only for other OSs.
Although being off-topic, a guy proposed a windows solution on a OS X question to ForceBindIp, speaking of which I had finally found this question but neither the accepted answer nor the "let's abuse HideMyAss' Secure IP Bind" one satisfied me because they apparently don't work on 64-bit processes.
My system is x64-based so are many processes, including the JVM, are 64-bit processes, thus unsuitable for the dll injection performed by the proposed programs.