Nothing in your schematic strikes me as wrong on first viewing, and you mention symptoms including an apparently low charge current along with a low charge voltage that doesn’t appear to change when feedback resistances are altered. Is that an accurate summary?
If so, it sounds like the sort of things that happens when the physical circuit differs from the schematic and/or one’s mental concept of it. Especially if this is a one-off, hand-assembled prototype you’re talking about, my first suggestion would be to take a very careful look at the physical circuit–look for solder bridges, open connections, things like that. If it’s something you’re seeing across a number of machine-made units then a systemic error seems more likely–maybe a hiccup in your layout…
If that doesn’t reveal a problem, I’d probe around to see if you can determine what sort of operational state the chip is in, and if the voltages present at key nodes are as expected. What are the diagnostic pins indicating? What’s the voltage at the CAPFB pin? Does the backup function work at all? Is the apparent charge current a continuous drizzle, or is it pulsed? Are the voltages at the assorted nodes stable, or is there drift, ringing, etc? …is the chip soldered on in the right direction…?
Every piece of info is a clue…