July - and my experimental batch of wine

I am planning on making at least two versions of kvass in the next week or so. Kvass is a traditional very low alcohol wine or beer. The beer version uses rye bread and sugar or honey, while the wine version uses berries (and sometimes ... beets). For the beer version I am planning on making a rye loaf and then toasting the slices and then soaking them in about 1 gallon of boiling water. To that porridge you add about 4 oz of sugar/honey, allow to cool and then add some yeast. As an alternative I will mash about half a pound of malted rye grains , half a pound of malted wheat and boil the mash to make 1 gallon - and add some yeast. To both versions I will add some hops for flavoring (not certain what kinds but I have a small bag of whole hops a friend gave me and may use these.
I also plan on making a berry version of the kvass - . This uses about one lb of berries and about 4 oz of sugar. The trick is to bottle the kvass a few days after fermentation begins so that a) the yeast is still in suspension - and so the drink is full of all kinds of B vitamins - and b) there is still a significant amount of sugar unferemented - so the drink is both sparkling and sweet and c) since the total amount of fermentable sugar per gallon is about 4 oz (at least with the bread and berries) the total ABV is no more than about 1.5% ABV. The grain version will have a higher potential ABV - closer to about 3 or 4%.
I intend to use a small quantity of Safale 05 yeast (a beer yeast).

So how long do you wait to drink it? Does it continue fermenting in the bottle, leading to a risk of exploding bottles?

That's the rub. It does continue fermenting in the bottle but almost every website that discusses /describes kvass suggests that a refrigeration is important; making a small batch that will be consumed in a short time is important (it is very easy and quick to make. Folk talk about how it can spoil after three or four days.. and that may be true given the low amount of alcohol in the drink) and using plastic bottles rather than glass makes the likelihood of bottle bombs less likely (much like the traditional way of making elderflower wine).. but it seems to me that a more simple idea might be to make the kvass in an airlocked carboy and so allow the CO2 to escape; but to use that carboy as the jug for storing the kvass and so the idea would be to bottle a batch of the kvass a few hours before you intend to drink it. That means it won't be sparkling but it won't be still.

For the record, I was in Leningrad and Moscow many years ago - before Glasnost - and you could buy kvass at street kiosks. It was quite delicious and very refreshing.