To be honest I'd try dry packing under the sill before you go cutting great lumps of concrete out to extend the gravel drain.
Dry packing is fairly easy and cheap with the added bonus that if there are other issues, which is a possibility, it is easily reversed.
Basically you'll need to get cement and sharp sand. Mix them together at the ratio of 1 part cement to 3 parts sand. If the sand is damp when you mix them together you probably won't need to add any water. Once mixed together grab a handful and try to form a ball with it, if the ball breaks apart you'll need to add more water, if it loses its shape or slumps you'll need to add more sand and cement. Once the mix is at the desired consistency push it into the gap and then pack it in with a piece of timber that will fit under the sill. You want you basically keep hitting it with the end of the timber to pack it nice and tight this way it will fill up all of the gaps and will therefore be water-tight.
OK that seems like a good place to start for the damp patch by the door!
I'm more concerned about the damp where the red circles are (hope my old skool MS Paint skills impress you!). Is it likely that the source/root cause is the same or another issue?
To be honest I'd try dry packing under the sill before you go cutting great lumps of concrete out to extend the gravel drain.
Dry packing is fairly easy and cheap with the added bonus that if there are other issues, which is a possibility, it is easily reversed.
Basically you'll need to get cement and sharp sand. Mix them together at the ratio of 1 part cement to 3 parts sand. If the sand is damp when you mix them together you probably won't need to add any water. Once mixed together grab a handful and try to form a ball with it, if the ball breaks apart you'll need to add more water, if it loses its shape or slumps you'll need to add more sand and cement. Once the mix is at the desired consistency push it into the gap and then pack it in with a piece of timber that will fit under the sill. You want you basically keep hitting it with the end of the timber to pack it nice and tight this way it will fill up all of the gaps and will therefore be water-tight.