A smoothing capacitor has little purpose in a battery charger because it will always rise to the same volt level as the battery being charged.
I think the DC resembles mountains peaks going as high as 11 or 12V. It needs to go that high in order to push 10 A into a 6 or 7 V battery.
Anyway if the recommendation is that the power source should be a few volts, then it could help to install a smoothing capacitor, since that will have the effect of leveling the peaks and raising the valleys. You might start with a Farad value of 3300 to 10,000 uF (microFarads). The volt rating must be higher than the peak of the waveform coming from your charger. 25 V is a reasonable, common rating for electrolytic capacitors.
I do not have experience with electroplating, but seems to me that the way to get more current is by (1) enlarging the electrodes, and (2) by cleaning them so as to make it as easy as possible for ions to come and go at the electrodes, and (3) by ensuring good connections capable of carrying several amperes, and (4) possibly by enlarging the cables to the electrodes.
I imagine the bath itself appears as a resistor to your power source (the charger). Does the charger have an ammeter? If not, then you can try measuring voltage on the electrodes while out of the bath, and then watch how much it drops as you put them in the bath to plate. That will give you an idea what is the load on the charger.
Whatever amount of current you desire, your power source will need to provide a high enough volt level, to push the current through the bath. It's possible that a smooth 3V waveform is better than a pulsed 10V waveform, I don't know.