Yes, I got another (earlier model) and removed and cleaned the rods. I will do that on this one as well. I do understand it's a dip pen, it's just that from the very first stroke it seems to write very dry, it write a long time with a steady but dry flow. I do think it's may well partially be that I didn't clean out the rods, as you say; and I'm going to try a different nib.
Try dipping the nib into a bottle of ink, to eliminate the ink well as the problem.
The ink may be too dry for the nib, or the nib may be too dry.
Either switch to a wetter ink, like Waterman, or swap/adjust the nib for a wetter writing nib.