FYI, last time I went through this (floating my car battery to top it up) I set it to 14.3V and went from about 20A initially down to a few 100 mA after 24 hours. This is a little high for a proper (always-on) float, but fine for this duration, and as you can see there was very little if any overcharging.
Electrolysis starts at higher voltages; you can't really charge much faster (than whatever the peak rate is, C/2 or thereabouts?) because the plates load up with bubbles, greatly increasing resistance. Dangerous, anyway (H2+O2).
OCV is around 13V and the extra voltage is required for charging, to overcome the overpotential of the electrode materials. Basically the overpotential consumes charge efficiency: you have to charge so-and-so above the electrochemical potential to make anything happen, and the difference is lost as heat.
Which is what makes lithium ion so amazing, there's essentially no overpotential and the cell voltage is entirely due to concentration of ions in the electrodes. So the charge and discharge efficiency is super high, it looks like a crummy nonlinear capacitor more than a cell.
Tim