Remember, the BCM controls the flashers
There is no flasher module. The BCM sees an input from the turn signal or hazzard switch, and turns the correct bulbs (front and back) on/off.
By the way, the bulbs or LEDs had nothing to do with you not blowing fuses. If you had direct shorts to ground with a power wire, the bulbs mean nothing. In addition, you said you had direct 12V LED replacements, so they had built in resistance to emulate a 12V bulb, to prevent a fast flash due to low resistance.
The new BCMs have some decent protection against shorts to ground.
Glad to hear it is fixed.