Well the manufacturer says that at 25°C the float current drawn by the batteries should be somewhere around 10mA.
I might need to feed some 400mA to an allways on solenoid which is not too picky about current, but needs to be connected to the battery in case the main charging supply gets interrupted. The power dissipation in the linear driver can be managed without any concern, but the main point is that the current to the battery according to manufacturers needs to have as little ripple as possible. When the battery is on float charge the manufacturer says that the current must not be alternating, that is a few hundred amps in an then a few hundred amps out alternating at 100Hz is a no go.
But even if my linear approach is not going to be implemented, how would I go about stabilising the feedback so that it does not ocillate and is not a square wave along with the mains feed frequency, just from the theoretical point of view?