HALLELUJAH!
So finally some awesome news.
It is now working as expected. The relays have started to engage/disengage properly.
After several days of just testing the MDX further, it suddenly turned out that everything seems to have “kicked back into gear” again.
The hardware bypass relays (which I initially suspected were defective due to running the device with the power supply that was too low spec for a long time) have now started to activate and deactivate as they should according to the information in this thread!
My suspicion is that something has gotten really confused up inside, or that for example the relays got stuck in some intermediate position when they didn’t get enough power to turn on/off fully, and that they have now started to work again after running the Mod with the correct power supply for a number of days. As if everything has somehow been “charged” back to normal.
I am thinking that running the MDX with the proper power supply for a few days has finally restored some components to their intended state/behaviour.
Thank you all for your troubleshooting help. I am as satisfied with the MDX as one can possibly be!
Ps. At first I thought that something else was also broken, because once the relays started working again, I experienced a high pitched whine when connecting a guitar to Input 1. There was no noise when using the Input 2.
But after a lot of additional troubleshooting I found that the CV/Expression port was set to CV by default. Switching this to Expression pedal (with nothing connected to it physically) removed the whine completely. Interesting, but I guess there was some interference creeping into Input 1 when this was set to CV without anything connected in that socket.