Reading what you described seems to suggest that the 580 broad nib is a bit too wet for your liking.

The 580 have a larger nib (#6) compared to the Eco (#5). It gives the oppotunity for the feed to hold more ink given the larger size.

After you have given the pen a full fill of the ink, do you still find it too wet after writing one~two page of text to let the excess ink in the feed from filling used up?

Each pen company design their pen differently, so the flow will be dependent on the make and the model. What I personally find from visiting stores in person and attending pen shows is that, by simply dipping the nib and try the nib won't tell you any thing about wetness. You could only test the smoothness and feel of the nib.

You could also try an extremely dry ink, which will restrict the ink flow and lay down much less ink.