Hello,
An Li-ion charger is basically just a two loop control system where one loop only controls at any given time.
It's basically a current limited voltage regulator with added trip points.
It sounds like you have the trip points figured out by using comparators with hysteresis, now all you have to do is design a voltage regulator and add current limiting.
The current limit will be set at 1 amp and the voltage limit will be set just under 4.2 volts.
With a discharged cell at near 3.0 volts, the current limit regulates the current to less than 1 amp. Once the cell gets near charged and the voltage rises, the voltage loop takes over and regulates the voltage at which time the current drops slowly until it gets to the required 'fully charged' current level at which time the charger shuts off.
Two more trip points you need:
1. Fully charged current level trip to turn off.
2. Safety timer to limit the max charge time for any one charge.