I don't think that a small hill (roughly 2*2km, and maybe 150-200m high) could support 8 streams flowing to the rivers. For example, Rome is very hilly as it is well known, and yet no stream goes from the hills to the Tiber (plus, the entire region is not particularly rainy).
The river as you draw it looks indeed better, but it does not make sense either to have it so narrow – this is longer than the Nile and draws the watershed of a continent-sized area, though not a tropical one, so probably smaller than the Amazon – nor to have multiple islands so large, I think. I should probably try to get a better shape for the river, though I am finding difficult to obtain a good result. It would probably be easier if it were narrower, but it can't be.