I borrowed and rode with a PM for a number of rides and compared calories burned based on joule output (using the accepted correction factors for physiological efficiency) to the HR formula in OP's method 1 and found I needed to multiply the HR formula result by 0.7 to get results close to the PM based calculations. With the 0.7 correction factor, the HR formula produced calorie consumption in reasonably close agreement with the PM results over a variety of rides including rides 25-100 miles in length, those with and without a lot of climbing, and fast pace and moderated pace rides.

This suggests to me that the HR formula can work well enough once calibrated to the individual.