Liquid flow control

But if I use zero pressure valves instead of a pump won't I have a similar problem? The more liquid is in the bottle the more pressure, and the faster it'll flow, right?

Yes but to a lesser extent.
May be you could make a simple pressure relief valve and or a regulater, but your pump should get up to a certain presser and nver go higher.
What if you used an empty bottle for as a reservoir tank.
Andy

Do you think it would be "close enough" to just use zero pressure solenoids? I mean, if I intend to pour out 1oz of liquid, am I going to get between something like 0.8 and 1.2 ounces?

Sorry, but my knowledge of pressure and plumbing in general is VERY limited. I've no idea how to use an empty bottle as a reservoir tank.

I dont think the flow rate between a full bottle and an almost empty bottle would be all that much diferant if you used zero pressure solenoids. You can test it using a manual valve and your bottle setup just dont forget the open air vent line.

Excellent, I'll give that test a go soon. Thanks!

Update: Did my flow tests manually (held my thumb over the opening, let go, timed). Looks like there's a fair bit of difference between the flow timings full vs. empty. I decided that I can handle that in the software (since it has to know how much liquid is in the containers to notify the user when to add more).

Since then I've ordered a single gravity flow solenoid and got it. It works perfectly! Now to just order 5 more, and hook it all up!

Thanks so much for all your help guys!