Hey guys,
I've just fixed this issue. With the information mentioned here about current consumption of the opamps I did a little research on current consumption of my current mod, then, after calculating which opamps combination would maintain the stock current consumption, I bought new opamps that can fit the board and replace the OPA1656 which are very current "hungry".
The OPA1692, have very low current consumption and can leave extra current available for the OPA1612 which are the best sounding opamps I have tried so far (from my point of view).
The result is no noise at the input #2 and a better sounding interface for a budget (yet, I don't recommend this mod to anyone).
Turns out opamps give you a color, which can not be qualified just by their specs, some colors are desired for some uses. Sometimes people like distortion because it sounds brighter and louder. Depends what you are looking for. Some users said here, "why did you mod this interface if it just sounds great", this is definitely a perception, which I didn't agree and found myself modding the interface.
Thanks for all the information you guys leaved at this thread, it offered enough knowledge to fix the issue. Yet I know there are many other aspects to be aware of when replacing an opamp, current is just an important one but not the only one.
Kind regards.