If the inverters are off, they'll accept AC charge current from my service panel and they do not produce AC. When I turn the inverters on, they stop charging and start producing 120v AC, but I can't get them to charge while producing passing through input AC to AC output.
I think that may be clearer way to describe your issue.
I am not 100% sure about this but your problem may be the inverter's second stage PWM chopper (or just inverter as you call it) was off before input AC was applied. When inverter (first and second stage) is providing AC output, then AC input is applied, the PWM sinewave chopper will slew its sinewave creation to synchronize to applied AC input. After this AC synchronization is completed (takes a minute or two) then you will hear the internal connect relays clunk sound indicating the AC input to inverter AC output is running in parallel.
Try having inverter running on batteries, before you apply AC input. See if this solves your problem. The problem may be if the inverter was off before you applied AC input it will pass through AC input to AC output but will not later be allowed to activate inverter PWM chopping to charge battery due to inability to synchronize inverter to AC input.
Another possibility is the inverter is not synchronizing to incoming AC properly. This could be a calibration problem with inverter's phase locking to match inverter phase to incoming AC phase. Inverter synchronization does not actually compare inverter output to AC input phasing. It modifies its PWM sinewave creation digital sequence based on AC input phase before connect relays are closed. There are software delay calibrations so when it does start up inverter it
should be in phase with AC input.
Some more technical details:
When you say 'inverter' it is a bit too encompassing when talking about a HF hybrid inverter. What you are calling inverter has two stages. First is battery DC to high voltage DC converter (around 180 to 300 vdc). Second stage is IGBT transistors that PWM chops the HV DC to synthesize AC sinewave.
For HF hybrid inverters, it is tricky to design a bi-directional battery DC to HV DC converter. Many of the Chinese HF hybrid inverters don't even try. They just put a forward one-way battery DC to HV DC converter for normal battery to AC output operation and a reverse HV DC to battery DC buck converter to charge battery.
I believe the LV6548 has a forward only DC to HVDC for normal battery to AC output operation and a separate paralleled HV DC to battery DC reverse buck converter to charge batteries. They cannot both operate at the same time.
When grid AC or generator AC input is applied, it will get passed through to AC output, through the internal connect relays. If battery needs charging it taps into the AC input feed to charge the HV DC filter capacitor, then the buck converter drops HV DC down to battery voltage. The forward DC to HV DC converter must be off during charging. If inverter was producing AC output before AC input applied, it must adjust its inverter AC phasing to match incoming AC phase before connect relay closes with input AC. If inverter is not operating before AC applied the connect relay closes almost immediately, as there is no inverter synchronization required.
There are two ways AC input to HV DC can be done depending on HF inverter manf./model. Simple-stupid way is rectifier diodes in parallel with IGBT output devices just rectify AC input to charge the HV DC capacitor. This method has a poor charging AC input power factor.
Second way to charge HV DC filter capacitor is to have output IGBT devices PWM chop, similar to sinewave creation process, and with PWM filter inductor it charges HV DC filter capacitor. This is more complicated as PWM chopping must be synchronized to incoming AC but provides a good AC input power factor during charging batteries.