It's only going to take cartridges, so IDK if that's "a lot" of ink, but how about a Platinum Curidas? Not everyone's favorite but the new gift set looks nice if you want a matte pen instead of a demonstrator.

I use mine for sketching, as I use platinum black cartridges (that I refill) and the light weight and width is nice for long sessions (I have big hands).

The real stumper to your inquiry is the lack of screw cap. For whatever reason lots of pens in that pricepoint are screwcaps. You could try a couple of cheaper slip cap options like a Platinum Prefounte, or Pilot Prera.