Battery charging over USB-C (using USB-PD?)
Your power requirements are well within the standard capability of Type-C port that uses special (but simple) pull-up resistor value on CC pins. The standard Type-C power delivery is 5V at 500/900 mA, (56k pull-up), 5V at 1.5A (if host pullup is 22 k, and 5V at 3 A id the pull-up is 10k. Therefore, completely forget PowerDelivery, and just use one of simple "CC controller" chips that usually detect the CC pulups, and can detect Chinese (DCP) port signature (D+ shorted to D-) allowing 1.5A. 

There are also some charging chips that combine all features in one IC, look for recent additions to Texas Instruments BQxxxxx chips portfolio. These chips will scale its current intake depending on signature they see from USB port, all automatically.