I finally solved the problem with the current limit detector. It takes not one but 3 transistors...
The first transistor detects when the shunt resistor exceeds 0.7V.
The second one short-circuits a 33µF capacitor to ground. When the current exceeds 200mA, the capacitor charges slowly.
The 3rd transistor is another "detector" that turns the LED on when the capacitor reaches 0.7V (it gives a nice level instead of an analog value).
The trick was to determine the RC constant... but back-of-the-envelope estimates worked well on the first try !
The ULN2003A is also wired so the relays can be driven by weak CMOS signals.