Since the bike runs the controller, circuit breaker, and DC converter have to be working so they should not need to be tested. When the battery power meter level declines that indicates that the Voltage of the battery pack has significantly dropped. Since the battery pack Voltage is dropping at around 6 miles it sounds like the battery pack has lost some of its capacity and in order for the scooter to have a longer range it would need to be replaced.
Bolts can weld themselves to battery terminals from the high amount of current that the batteries produce. When this happens a little bit of smoke will be created but not a lot. If a positive terminal from one battery contacts a negative terminal of another battery the two batteries combine into a higher Voltage battery pack. Since the batteries were already in a battery pack configuration when the terminals welded together it must not have changed the Voltage of the battery pack at all, or not enough to disable the bike.
It seems to me that at least 1 more battery is bad. remember that battery can measure 12 volts but the life is also measured in Amps. if the battery discharges quick then the life is gone. If you bought the scooter new then batteries should be under warranty. if you bought it used then I would replace all 4