I'd go with an inverter/charger. Why have the extra wiring? Or the extra cost? They really don't fail that often
But, before replacing that inverter, I'd suggest doing a small few things to check the hypothesis that the inverter is bad. That is a bit of an odd failure mode.
Most breakers are relatively slow to blow -- it takes over current for a while to cause them to trip. How long depends upon how much current. There is basically a curve.
So, if it is charging for "a while" before tripping, the longer "a while" is, the less "over current" it probably is. But, it doesn't sound like a short or near short.
If you have one, I'd put a multimeter current clamp around the supply wire and check to to see what it is drawing. I'd compare that to the rating on the breaker and to the rating on the manual, just to get a sense of the landscape. Is it drawing more current than it is supposed to draw? Or just more current than it is currently set up to draw? (You probably know this, but don't change to a larger breaker unless the unit's manual says it is rated for it -- and the wiring is of a sufficient gauge. Since it is AC on that size, the gauge is more dependent on current than length).
Where am I going with all of this? Once you get a sense of the landscape, I'd check the connections to make sure they are mechanically sound, free of corrosion, etc.
-- Supply to panel/breaker
-- Supply to inverter
-- Inverter to battery (if there is a switch in between, inverter to switch and switch to battery)
-- Ground path between/among all affected batteries and batteries to inverter.
I'd also check to make sure the batteries are watered, then turn off the charger, load them for a bit, and then check individual voltages, disconnecting the ground from each to check each one in a bank, if needed.
If the connections all really look good, and the batteries look good, I'd start to dig deeper. I don't know that inverter-charger, but if it has a multi-bank capability, I'd try isolating to one bank at a time -- on many chargers all output need to be used, so, if that is the case, normally one can move the battery-side wires all to one battery.
Next up, if you've only got one bank, or isolated the problem down to one bank, I'd reduce that bank to a single battery and see if I could get it to work with just one. The idea being to try to isolate the bad battery within the bank, or the bad battery connection, etc.
Where I am going with this is that...if a connection is getting high resistance from corrosion, loosening, or mechanical damage, etc, it could make the charger think it is at a lower voltage for longer. This could keep it bulk charging (vs absorption or float) for longer, drawing more current for longer. If things were already close w.r.t. the inverter draw vs the breaker size -- it could trip where it might not have before.
It could be as easy as a crimp connection that has gotten loose, gotten corroded, or been pulled out a bit or a nut or screw terminal. Or, gulp, a wirenut (ouch) that got loose. Especially if household stuff was used anywhere.
Similarly, if there is a bad battery that isn't coming up to voltage, or coming up to voltage as quickly, it could be doing the same thing.
In either case one would really want to fix the root cause of the problem vs replacing the inverter (even if replacing the inverter seemed to cure the problem by having a different curve, or being more efficient and drawing less current, or getting a new breaker and bigger wiring).
I've bought new things on more than one occasion to end up finding the real problem only when undoing things to redo them during the install -- more than once!
