The main culprit for the internal supports of your print being stringy would be the thickness of the layers put down into the infill. You can increase this setting in Cura under Fill settings.
The most common issue with infill is the infill speed being set too high. This is normally fine because no one will see the infill, but it can cause problems for the surrounding edges and structural support. You can change this setting in Cura under the Advance tab and Speed category.