Having designed machines which fill bottles, looking at the videos I'd say your outlet tubes from the solenoids are way too long.
You won't get a sharp on/off flow - there will be fluid left in the outlet tubes which you have very little control over - some may stay in with its own surface tension, some will drain gradually as air enters the tube.
I've had great fun in the past trying to do a similar thing but for a totally different application (medical filling applications).
I've not read the whole thread but .......
Some solenoid valves require a slight back pressure to open quickly and effectively
The more pipe after the valve, the less the accuracy of the fluid dispensing. A short burst into an empty tube will result in an empty tube as the fluid will dribble down the side of the tube, a long burst may result in a full tube with all air expelled but the surface tension / vacum may hold fluid in the tube
If the liquid is pressurised, consider one way valves in the outlet tubes. Pressurising wouldn't work very well though as you ideally want the fluid to drop out under gravity.
If you took the pipes off the bottom of the solenoids and lined them all up next to each other (at the expense of resolution), this would take away a lot of the variables associated with the pipe issues when testing.
I've worked on pumped systems, pressurised systems, gravity fed systems, piston systems, peristaltic systems, vacuum mixing systems and weight based systems and had to meter fluids down to a millileter and fluid is not the easiest of materials to work with
(add in varying viscosities which themselves vary based on the temperature of the workplace and you end up pulling your hair out)