You have a couple of options. One is to get a different ink, as you note. The other is to use a different etchant. Both work.
If I were you, I would get samples of several "inks" that I could get easily, and swipe a little stripe of each on a piece of copper clad, dry the ink, then etch it. The good ones will etch nicely, the bad ones will go away or not etch well.
Screen printed circuit boards have the issue that the ink must cure fairly quickly or the air to which the un-covered copper is exposed will oxidize, and then it won't etch where it's supposed to.
I experimented with screen printing long ago. Works, but is messy. I found that presensitized photo PCB stock works very well indeed, has high resolution, and about the same amount of messiness as screen printing, in addition to being quicker - no curing time.
UV cured screen inks work GREAT, but you need a UV curing source. You also need a similar UV source for exposing photo PCB stock.
A big issue for me is that photo PCB stuff is already cleaned and ready to etch - I don't have to do the initial scrubbing that I would with screen printing. Saves a step.
Just some random thoughts.