Paedocommunion and communion wine

In this post I'm not going to discuss the pros and cons of paedocommunion. instead, I'm going to raise a related question. 

I take it as rationally indisputable that the NT church used wine rather than unfermented grape juice in communion. This means that if you espouse paedocommunion, and if you celebrate the Eucharist with biblical communion elements, your children will be drinking wine. The question, then, is whether or not that's problematic. I imagine a proponent of paedocommunion might respond in one or two different ways:

i) He might restrict participation to children eating communion bread rather than drinking communion wine.

ii) Perhaps he'd say the quantity of wine is so small as to be insignificant.

iii) However, the quantity of wine which the communicant imbibes is, to some degree, affected by the mode of administration. Many evangelical churches administer communion by filling plastic thimbles with grape juice. That effectively regulates the quantity of liquid which each communicant imbibes. 

However, in liturgical churches, communicants drink from a common chalice. That, of course, raises the additional question of whether a common chalice is a more biblical way to administer communion. 

If you use a chalice, then it's up to the individual communicant to regulate his intake. 

iv) I don't know the average age at which European parents usually introduce their children to alcoholic beverages. I expect that's underreported. Even if there's polling data, what they tell a pollster and what they do in the privacy of their homes might be two very different things.