'At 400 watts, your inverter is just barely powerful enough. 3 Amps times 120 volts equals 360 watts.'
I'm just going off of the numbers you posted. It is very possible that either:
A) The numbers printed on your charger are not accurate.
B) Your battery and charger are much more powerful than what those other people are using.
C) Their chargers are able to work with lower current for longer time while yours does not.
D) Your first guess, that your inverter is crap, is accurate.
Or:
E) E-bike chargers are rated for the amps provided at the bike battery voltage level.
So a charger rated at 3 amps and the e-bike battery is rated at 52 volts...power used by the e-bike charger is roughly 156 up to maybe 175 watts...(which should be easy to handle for a true (continuous) 400 watt sine-wave inverter, assuming it is wired adequately and working properly)
I mentioned this calculation in post #39.