Then all the remaining trains hit the red signal, block a while and then go somewhere else. Likely most will pick the same destination again and again and again. By the time they have even half sorted themselv out the nearest station is free again restarting the problem..

I have about six mines ...

In my experience simple "disable if station resources below X" logic works well if done properly. More precisely, I keep the station closed until each wagon can be filled independently, using some balancing logic to ensure even distribution into the buffer chests. Trains do not actually wait on red ...