Electronic – AP5002 step-down switching regulator loop stability

Problem, parameters

I have an 5V output power supply, with 2S LiPo input (6-8.4V), implemented with AP5002 (PWM control 2A step-down switching regulator, docsheet), and for the life of me, I can't make it stable. The PSU is chirping, dropping voltage irregularly, and in general shows a chaotic output voltage.

This is at around 300mA load. The full load my circuit draws is 900mA (mostly LEDs).

The initial circuit is as follows, I'm using ceramic capacitors both for input and output caps.

Note: C40 is far from PSU, close to the battery.

Ground plane with green:

My attempts

I started calculating the feedback loop, but I neither have enough experience in this, and also several parameters of the AP5002 are missing (eg. the internal amplifier circuit gain, transconductance, etc…). I calculated however the zeros and poles of the output filter network:

$$
W(s) = \frac{U_{out}}{U_{sw}} = \frac { R_e C s + 1 } { L C s^2 + R C s +1 } \\
p_{1,2} = -109 +-4.545 \cdot 10^4 j \\
z = -9.47 \cdot 10^6 \\
k = 218
$$

I started to implement a compensation network based on this docsheet of a similar regulator by ST. The most stable configuration I was able to come up with is this:

The values again (close to the theoretical values calculated based on the ST doc):
Rs=160R
Cs=2.2nF
Rf=6.8k
Cf=2.2nF

This was better, but became unstable at around 400mA load. I tried countless variations of values, even soldering in 47k trimpots for Rs and Rf to be able to sweep values from 0-47k. No success.
I also tried a 22uF tantal cap for output filter, hoping the larger ESR will make a diff, but nope; the loop behavior hasn't changed.

Any comment or advice is appreciated, thanks!