I have added coolant twice over the last 2 years to my M3 vert. I had to do this every once in a while to some E36's I owed but not all of them. Your use is higher than I have buy a huge margin.
I found it almost impossible to detect a leak. I added dye as well to my 325 that was loosing coolant. I did find it and of all places it was a very small leak coming from my expansion tank overflow hose that goes to the expansion tank from the radiator, the small one. I also found a leak on another 328 I owned that was also impossible to find but found the phenolic to aluminum alloy seem was barely leaking causing the issue.
My advice is to put something that can catch anything that falls in your garage so that even a trace would show up. I hope for your sake that there is something because otherwise this is sounding like a head gasket leak.
There are times when you don't see oil in the coolant or coolant in the oil because the breach is leaking into the block or head and getting burned at a very slow rate.
Last thing to try is to pressure test the coolant system and let it sit for a while like an hour. If the pressure goes down maybe you can find the leak or it is leaking into the engine...