Hello there Willen,
Are you sure that is the correct schematic, ie where did you get that from?
I ask because according to the data sheet and related app notes, that would only put out about 50ma or something small like that, and that is due to that 5 Ohm resistor which going by the data sheet would have to be more like 0.5 Ohms. Also the inductor values seems way too small, with the typical lowest value maybe 200uH not 20uH, and 2mH would be typical. We could look at this more though.
With that in mind and the fact that you dont like to desolder parts on PC boards, maybe it would be better if you just tried to add an input series resistor to lower the output current to the cell to be charged. This would not be hard to do but would require a power resistor, and you may have to try a couple different values.
If the input voltage is really 12v then a 10 ohm resistor would drop 5 volts at 500ma so that would only allow 7v to reach the chip now, which may just be enough. Unfortunately if the input power supply voltage changes then so does the current, so hopefully it doesnt change too much, and if it does not change too much it would still be ok.
If 10 ohms is too much then of course lower it a little to like 9 ohms then try again. If 10 ohms is not enough then try 12 ohms and try again, etc., etc.
Hopefully this does the trick and you wont have to modify the actual PC board which i see you dont like to do and i dont blame you. If you do have to do that though, the resistor to change would be that "5 Ohm" resistor but after looking at the data sheet i cant see yet how it can really be 5 ohms. If it was 0.5 ohms that would make more sense, and then you could try raising it to 1 ohm and that would halve the output current from what it is now, and of course a little less than that would mean a little more current than half.