I think I came to a solution. I will use current mirror with aditional bypass transistor, which can whitstand 6A of current in case, no string is connected, so all the current passes throuhgh this transistor. I draw a circuit in LTspice and simulated it and it works. Please, ignore part values, because they are just for a test. Do you think this will work as expected?
I guess, I'll really have to omit the protection and maybe just use some current mirror to equalize currents. I hope that non of the leds dies, or at least just one string.
Exactly how would resistors in each string equalize currents through leds? I am talking about configuration with constant current power supply and multiple parallel strings of series leds with series resistors?
Oh, and btw, how about this circuit for equalization of current?