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Looking for a 2-cell LiIon charger - with an unusual set of features

I have a very strange set of power management needs on a new product I'm developing.

I need a charger for a single-cell Lithium-Ion battery that is meant to be used for backup purposes. The primary power source in the system is a two-cell Lithium-Ion battery pack, which is swapped out when it drains. The system can also be plugged into an AC charger.

I need to be able to pull just a small amount of current from the battery pack, but be able to charge from the AC source at a much higher current. Otherwise I'm losing a tremendous amount of efficiency. My system's power draw will be at least 2 A or so.

Everything I've found has been close to, but not quite, what I'm looking for. Many of the charger ICs with a second input only allow that input to go to 7 V or so before the overvoltage is triggered, while the battery pack would reach 8.4 at full charge. Some with the second input don't allow enough current on the second input. I have a power path selector chip I can use which would let me use a single-input charger, but I still need to be able to select between high-current mode (1700 mA) and low-current mode (~200 mA) depending on where the power is coming from.

I don't care about efficiency while on the charger, but since it is a concern while going from the pack to the backup, I do want to aim for a switching charger. Bonus points if there's a gas gauge integrated in the device, so I can knock one more component off of my BOM. Chatting with and emailing TI have not been successful at helping me.