Your Italian charger does sound like it isn't up to snuff. A
shore power charger should peak at 14+ V before it drops back to about a 13.5 float voltage.
How big a charger depends on what is the
power source and how big a battery bank that you have.
With 4-4Ds you have about 800 amphours and general practice is to not charge at over 25% of the battery capacity for flooded cells. So that criteria limits you to 200 amps.
If you are
charging with
shore power over night then almost anything will
work as you have many hours to get the job done. Your 30 amp charger would do the job if it had a good three step algorithm, which it seems not to.
If you are
charging from a genset, then you want the largest charger that your genset can provide
power for. A 100 amp inverter/charger typically pulls 15+ amps AC at maximum output, sometimes more for inefficient ones. That is about 1.8 KW and any built in
generator can handle that much, but the ubiquitous
Honda 2000 EU can't continuously. In that case the best you can do is about 75 amps.
David