I am not sure what is bothering you.
Yes the internal resistance is negligible so forget it. The battery will clamp the voltage, but what voltage? is that confusing you?
The emf of a battery ( virtually the same as volts as the internal resistance is low) depends on electrochemical reactions . A battery on charge will have a higher voltage than one on discharge and the actual voltage depends on the current and state of charge.
During charge the voltage will rise and also at any instant forcing more current will also result in a rise of voltage due to gas formation on the plates ( surface charge). This has nothing to do with internal resistance ( an order of magnitude smaller and you won't even see it at normal currents).
"But why is the measured charge voltage higher than the battery voltage? In my experience, at any given moment a higher charge voltage will result in a higher current and that doesn't make sense if the voltage it's really clamped."
I think this is where you are confused, What is charge voltage? your idea of it seems strange. Surely the charge voltage is that between the battery terminals on charge.
I have a feeling you are considering constant voltage charging circuits and are considering the charge voltage to be that of a constant voltage source that you connect to a battery. This mode of charging is not the same as current limited charging from wind or solar.
In this case you can use a constant voltage over a limited range and the battery will adapt but you can't cover a wide range of charging conditions without having current limit to cater for a low battery. With constant voltage charging you can only deal with a battery whose terminal voltage is kept within close limits and the battery surface charge mechanism will regulate the current to suit ( basically a battery on float or very near it). A low battery will draw excessive current and you will have to limit it in some way. As soon as this happens the battery terminal voltage will not be that of the source emf and you must consider the charging voltage to be that measured on the battery not the source.
When we talk about a battery clamping the voltage we are normally looking at wind or solar or some other current limited source. In the case of wind the open circuit source voltage can be very high ( 100's of volts) but as soon as you connect the battery it will drop to battery voltage and the mill will dictate the current ( not the battery).
The battery voltage will still change with state of charge ( not internal resistance but surface charge). The battery will be an effective clamp until fully charged then things get out of hand and you need an external voltage limit to prevent excessive gassing.
Flux