I don't know the dwell characteristics (coil ON time) of the Dyna 2000. But, when the coils are being charged up, they will draw 4A rather than the 2.4A the stock 5 ohm coils do. Considering the alternator makes about 5 amps at normal idle speed (it's a 12 amp alternator when spun up.), it's not too surprising the battery is depleting, especially with other loads like lighting added to the power draw. The stock bike draws about 10 amps with lighting on during run time.
The Goldwing has low ohm coils, but they only give full battery voltage to the coils when the starter motor is engaged. Otherwise they are given 6V during run time with an inline voltage drop resistor. Contact Hondaman for a resistor kit to tame the excessive power draw of the 3 ohm coils, if you insist on keeping them.
In the mean time, characterize what your bike does:
A -- Fully charge a known good battery. Let it rest for 2 hours, off the charger, and measure the battery voltage. (Target is 12.6-12.8V for lead acid type.)
B -- Start the bike and measure the battery voltage at idle, 2000, 3000, 4000, and 5000 rpm. Note how the voltage is trending. This tells you if the battery is recharging or depleting, and what RPM is need to keep up with the bike's electrical loads.
C -- Repeat the measurements of B with lighting off (pull the lighting fuses if need be).
The above tests identify charging system success, failure, or degree of "faulty". The success voltages are listed in the Shop manual for lead acid applications. If you have a lithium type, get state of charge information from their manufacturer. The LiPO4 types should top out at 14.6V IIRC. But, if voltage readings trend downward, then it is depleting, and the charging system isn't keeping up with the power demand.
Cheers,