Measuring the cold resistance of a light bulb doesn't tell you its operating current. The resistance of a light bulb increases quite a bit as it heats up enough to create light. A fixed 1.5-ohm resistor, at 13.3V, would draw 13.3V/1.5 ohms = 8.9 amps of current. That represents 13.3V * 8.9A = 118 watts of power, which is far more power than even your headlight draws. In reality, once it's up to operating temp, a 12W bulb will draw just about an amp from the vehicle's ~13.3V operating voltage, with its hot resistance somewhere in the 13-ohm range.
Try this: Put one of the old right-hand signals back on, say the front. Verify that it works when you turn on your right blinker (it may operate fast because it's only running one light, but it should operate). Put your voltmeter on the leads going to the right rear signal, and see which one goes positive when the signal blinks. Attach the new signal with that polarity. It should operate with the front one. Mark the wires with tape so you can get it re-attached correctly with 100% confidence. Now do the same procedure for the front: Put the old signal back on the rear, verify proper operation, check which front lead goes positive with the rear signal, attach the new one, verify it works, mark the wires. Now attach both new signals; you should, at this point, have 100% confidence they're correctly polarized.
If at this point they don't work, it's because the blinker requires more load to operate correctly...LED turn signals don't draw enough current to make some blinkers work at all, other blinkers will operate but too fast. You can then either change the blinker to a more modern one that blinks properly even with a light load, or add resistance (probably something in the 15-ohm, 15W range would work well) in parallel with one of the left-hand signals, and one of the right-hand blinkers. I'd suggest upgrading the blinker instead of adding parallel resistance.