Aren't the linked peristaltic pumps a little bit too slow for this purpose? It would take 3 minutes to fill 300ml of soft drink on top of 200ml vodka.
Another tech thats been popular over the years is just tipping the bottle, which has the advantage of putting on quite a show and the disadvantage (or maybe not?) of splashing. You need a beefy servo because the center of gravity and torque are going to vary as the bottle empties.
Finally another tech often implemented in these robots is running the receptacle on an accurate-ish lab scale. Gram level accuracy is probably good enough although 0.1g accuracy would be better.
Its an old idea thats been around since at least the 80s home computer era, its been fun watching reimplementations and new ideas and new techs.
WRT to quality valves if you have a slow leak in the air input valve, even just a drip per minute, you'll slowly drain the bottle while it sits there. A more complicated arrangement with more valves can vent the bottle when its not supposed to be pumping which helps.
Your scale idea is excellent and I've seen it done. If you're sufficiently motivated its a great platform to play with PID controllers or at least PD (not I) control theory.
For a literature search I've seen this kind of machine in make magazine maybe in the 00s or at least a couple years ago and in some 80s era home computer magazines. It fell out of favor in the 90s or maybe I wasn't paying attention.
Advanced systems put a slight vacuum on the delivery hose to prevent dribbling although there's obvious cross contamination fears. From memory this was part of the reason the "tip the whole bottle with a R/C servo" guy took that approach, side from being visually more stunning. I remember that guy writing about an air traffic control issue where you can't have the neck of two bottles in the same airspace simultaneously, so extra delay timing is critical, can't immediately drop one bottle at the same instant one is lifting up.
I also recall reading about a design involving "hit the wine-in-a-box button with a servo horn" although that had variable flow rate problems and splashing issues, which might be worked around.