Thanks for your support. 
I know where the noise comes from - it's the amplified noise from the machine's own audio outputs (psg and ppi). I am waiting for the 4069 (original) chips to see if they solve both problems and then I will make a decision on how the final version of the schematics should look like.
I also noticed that the CXA2075 chip gets quite hot, checked all inputs but found no excessive voltages on any signals. The chip works for many hours without a problem. Anyone has an idea why it would get so hot?
The project is now complete! I've just assembled and tested the final version of the board. It works as it should, at least in my Panasonic A1F. I haven't tested it on any other MSX yet, but I presume that it should work on all other compatible machines. But there's no 100% guarantee until this is tested by me or someone who gets the DIY kit.
Here's the photo of the assembled board:
At the moment I can only provide 4 DIY kits for sale as the 4069UBF chips that I got from China were not new and at least one of them already appeared to be faulty. So, I will provide 2 of those chips per kit in order to be on the safe side. Those who already contacted me by e-mail will be served first. I also will have a few bare boards for sale. Contact me my mail if interested to get a board. One board per person only.
When waiting for a reply from me, please check your SPAM folder as some of my replies may end up there.
@STT and @daniel683104 - please contact me by mail if you want your kits. Otherwise they will be sold on "first come - first served" basis. Only one kit per person.
It's still possible to install 74HC04 instead of 4069UBF (that are only available as used). To remove interference from the audio channel it's necessary to install a 68pF capacitor between pin 3 and ground. Here's the picture of the mod:
