I'm not quite sure what the purpose of the pressure gauge and needle valve on a 2L pop bottle system would be...
In any case, using vinegar and baking soda will generate CO2, but it is uncontrollable. CO2 gas will just be generated, and I suppose with your product it "should be" controlled by the pressure gauge/needle valve. However, 2L bottles are not designed to hold a significant amount of pressure, so you may find that your bottles explode instead.
The yeast method consumes sugar and produces CO2 as a byproduct of metabolism, and this method generates CO2 more slowly, but also over a longer period of time (weeks versus instantaneously for vinegar/baking soda). Because of this, you do not need to put a pressure gauge/needle valve on it, thereby not stressing the pop bottles to enormous pressure.
I would avoid using the vinegar/baking soda method. If you want to avoid using DIY CO2 using yeast due to the smell/hassle/etc, then I would suggest you take a look into pressurized CO2 (take a look at the articles that I have written (linked in my signature) for more information).