Schematic review LiPo charge load sharing with booster
UPDATE: If I were to design a custom board, I think I would go with something like this based on LTC4412 and LT3651:

More details in this post on e2e.ti.com

ORIGINAL ANSWER:

I had a very similar task. Here's what I ended up doing, and I confirm that it powers Odroid XU4 (including under full 100% CPU load, ~3A) and charges battery at full charge current.



I had to drive the FET gate with output from a voltage supervisor, otherwise when unplugging power, the FET would turn on way too late, and the load would die because Vload &lt;5v.

Also, NCP30x supervisor could not drive the gate directly (?), so had to put another P-FET that between main P-FET's gate and VBAT, and use an active-high supervisor NCP301HSN, pulled up to VBAT.

Also, make sure P-FET Ron is low, like in DMP4010SK, otherwise Vload will droop under load spikes.