I procured a used Trace 4KW inverter identical to what is in my boat and have wired it in as charger only. This has bumped my charge current from 115 to 205 amps max when at bulk rate. As they do not communicate with each other one will always come off the bulk rate first, if I wish to put it back on bulk I have to shut it down and restart it, a simple matter. I only use this second charger when on the generator set, any other time I can use long term shore power to bring the batteries back up. I have read that another way to keep two independent chargers going at max bulk rate is to put them at each end of the batteries.
It is probably a good idea to run both chargers on AC shore as well, having the right rate of charge for depleted batteries helps their longevity. Achievable target charge rates are 10 to 20% for flooded and 10 to 30% for AGM. Considering the bulk rate, from experience, batteries will stop their bulk rate between 80% to 85% state of charge and earlier for older sulphated batteries. Once this level is reached, one charger or both chargers will slow down and go in absorption rate. Resetting a charger forces the unit to go in bulk mode regardless of state battery. I am not sure that is advisable or necessary.