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I can do that (that's how I usually set the limit screws, is there a better option?). If you look at the cable on my picture vs yours, I think it's kinda obvious that, as the cage moves towards the lower gears, it reaches a certain point where the cable is bent in such an angle (like in my pic) that pulling on it further doesn't really move the mounting point any further outwards, but only tries pulling it upwards. Hope that's somewhat understandable.
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that's how I usually set the limit screws, is there a better option?)
Me too, so let's hope not 😀
as the cage moves towards the lower gears, it reaches a certain point where the cable is bent in such an angle (like in my pic) that pulling on it further doesn't really move the mounting point any further outwards, but only tries pulling it upwards.
It does seem like a design which relies on the dropout not exceeding the specified thickness, as there's basically no margin for over-travel at the low gear end. I had the opposite issue with my MTB, dropout too thin meant it wouldn't reach top gear. Obviously, a shim solved that for me, but you're going to find it harder to get a negative shim.
Unhook the cable and see if you can get the upper pulley in line with the big sprocket by pushing the dérailleur manually. Once you know it will go to the right place, you just have to find out why the cable won't take it there.