Reduce and compute flow in self designed pen

I am currently designing a simple pen for drawing with different types of liquid varnishes. My current design has a tip at the bottom side of the pen (blue) and a tank at the top side where the varnish is filled in (red). This varnish flows through a 0.7 mm hole in the tip. The drawing works so far. But the problem is, that it flows too quickly such that I have to draw extremely fast to prevent it from dripping. The main goal is now to reduce the flow/pressure in the tip. Unfortunately, the tip is not manufactured by me so that I cannot change it. But everything else is printed with a 3D printer and can be changed.

I thought about two different design changes. Option 1 includes a small channel between the tank and the tip. I printed this option with a channel size of 1mm, but I didn’t help. Maybe the channel was too big. Option 2 added cap on the top side of the pen. I hoped that it would reduce the pressure by letting less air in, but again this did not really help. The size was 1mm which is maybe still too big. My question is if these changes help to reduce the pressure on the tip. Are there any other physical tricks to reduce the pressure/flow? Would it help to make the tank wider/narrower?

In addition, I wanted to ask if it is possible and how to compute the pressure on the tip with these designs.