"I will definitely finish this over the next months" heh.. no.. I lied.
But I got back to it and completely revamped the hardware and just finished a new prototype.
The results I get with this new prototype are a LOT more promosing than what I got so far.
Instead of the old ATtiny setup I used just an ESP8266 and a MCP8421 18bit ADC. I found that I don't need the 18bits but given that the ADC is fairly accurate I can get a pretty clean reading at 12 bit and 8x amplification (using the built-in amplification).
This is how the new prototype looks like:

And this is a sample reading. Having a differential reading makes a huge difference. I didn't think about it before but with AC current it doesn't really makes sense to do anything but a differential reading because otherwise you get nothing at all half of the time.

What I also changed was the resistor in the CT clamp. By standard the 30A version I got has a ~38 Ohm shunt resistor. The smaller the resistor the higher the resolution per mA but what I really needed was to scale up what I get so I soldered a 50k Ohm resistor in there and got a much better respond to smaller currents as the voltage drop increases. Should be noted that I still have a somewhat half knowledge in this area but the result was what I wanted.

Now I will run some extended tests and if all goes well I will incorporate the new sensor board into my old software and write an algorithm for my machine. With the values I get this should be fairly easy. I found that every washing machine behaves completely different so you will always have to write a new algorithm for a new machine or implement some sort of end-user assisted machine learning algorithm.

I also made a schematic of the new board if anyone is interested. Maybe I make a PCB later on when I finished testing.