If you want to increase charging speed but you need long wires/traces between the charger IC and the battery, you may want to look for an IC which has a "voltage sense pin." This will read the voltage at the battery, so that the IC can actually increase voltage above 4.2V to compensate for the voltage drop across the charging conductors. A charge IC/circuit can't do this blindly without possibly damaging the battery; it needs a low current voltage sense connection.
"Voltage sense" is what I call it in my head, anyway. I am pretty sure this is what it is called in the industry when it comes to voltage regulation circuits. But I have a way of misremembering things to fit my own thought process.
At ANY rate, there is no way you are going to hook up a dead li ion battery to a charger and for the terminals to instantly show 4.1+ V per cell. That would mean it is at least halfway charged, instantly. So with a voltage sense circuit, the scenario you just described will still happen. It may be your battery is in the constant current stage, limited by a maximum amount of current. This is perhaps why you are recording 4.1 V per cell at the IC output, rather than something that would round up to 4.2V. If you had current sense line, this wouldn't necessarily change. 7.8V recorded AT the battery terminal may simply be the voltage which results in the max charge current. It's in the constant voltage phase, where the battery is like ~ 2/3rd charged, where a voltage sense will decrease your charge time.