So after having some trouble with the Solar Stage’s LT4071, I took Greg’s advice and recreated the LiPo charge circuit on a breadboard. I used a proto adapter boards leftover from my attempt at breadboarding the SPV1040 solar boost (see why breadboarding high freq circuits is trouble).
After following the instructions for the charger IC’s eval board, it powered up and switched to supplying the battery through VCC after the power was removed. This was verified by watching impedance of the HBO pin, which went to 0 Ohm when it hit the charge cycle.
Moral of the story: examining sub-circuits is useful and rewarding!