Okay, I got the new flasher units, and the rest of the LED bulbs today. The flashers now work perfectly with the old incandescent bulbs and with the LEDs:
Of course, the tabs on the flasher on the xD had to be clipped off to fit it -- they changed the mounting slightly...they are the two bits sticking out the back in this picture. The circuit board is completely different; though the two relays are still there. The IC chip is under the "U1" circle with epoxy on it, and there are four diodes, and a resistor on the top side.