I usually can't bear to cull my seedlings, so I would let them get a set of true leaves then take a fork and gently loosen clumps of two or three seedlings and plant them into their own pots, maybe Styrofoam coffee cups. You could probably do it sooner if you're very careful. You could also carefully turn the whole pot over into your hand and separate seedlings. As the clumps of medium fall apart, just work carefully with each seedling(I use tweezers and lift by the leaves, not the stem). If you're of strong will(I am not), just let them get bigger and prick or cut out the weaker plants. HTH

I love your pop bottle planters - have not seen that one before! I'll be trying it!

I also hate to kill off my little seedlings that I coaxed into life. But I would transplant sooner rather than later.

I have a friend who always plants basil thick and never thins. It works for her.

Just came cross your post, Zora. I expect you already have dealt with your growing seedlings, but I thought I�d describe my technique. See the link below for a photo of some of my little herb & flower seedlings at Flickr.
Over the years, I have started thousands of plants just as you did (though I happen to use pots, not pop bottles--but certainly your containers are just fine!). I learned this technique when I worked at a small, family-run nursery; my boss started all her seeds for her commercial nursery as well as her husband�s truck farm in paper strawberry boxes (pints and quarts), starting literally thousands of plants in this way each year. I was the only person she employed as seeder & transplanter (she did much of that herself), so I have had hours and hours of experience doing this! After she retired & closed the nursery, I continued at home the techniques I learned, but on a much smaller scale!
I learned always to water the pots from the bottom. I set mine in a dishpan with a few inches of liquid kelp solution (I use Maxi-Crop per label directions). Once the seedlings have grown their 2nd set of leaves (first true leaves), I allow the pots to get fairly dry, but not to the point that the seedlings become wilted or stressed. Of course, I have the cell packs prepared: labeled with the plant name & variety and filled with moist soilless mix that I make up (a blend of peat, vermiculite, perlite, coir, and my worm compost). I also have a quart bowl of extra potting medium within reach.
I knock the chunk of seedlings out of the pot, cradling the top of the pot in my left hand (I am right-handed) and sharply smacking the base with my right. Sometimes the soil block takes some persuasion, but the roots are all intertwined and all should come out in a block. Some types of seedlings fall apart easily once out of the pot, others have to be teased apart by gently tickling at the root ball. Don�t squeeze the stems to separate the individual plants or they may be killed; try to handle them carefully by the leaves. This comes easier with practice! Using your fingers, create a small planting hole in the cell pack (or a pot), lay the seedling into the hole, scoop up a small quantity of your soilless mix from your bowl of extra mix and fill the hole in, firming it gently around your seedling. Once the cell pack is complete, set it briefly into a pan of water as described above. The kelp solution helps avoid transplant shock and adds a very light bit of fertilizer. Leave it in the water only for a moment; when you lift it, the surface should not be wetter than the mix you used, but the container will feel heavy and water will drizzle from the bottom. That�s enough; the water is down where the roots need it. Too much water invites damping-off as well as fungus gnats!
Set your planted packs into a flat with drainage holes; this may be set into another flat with a solid bottom. Put it under lights (or into your sunny window) and that�s it. These usually will not need watering again for several days. Again, lift the container: if it feels heavy, it needs little, if any, water.
Depending on what and why I am growing (sometimes I plant for friends or relatives) and weather & timing, I often will pot on once more from cell packs into individual pots.
I always plant lots of Genovese basil as everyone I know loves it. And it is such a pleasure transplanting these & other herbs since they are so fragrant! Best wishes!

Here is a link that might be useful: Herb & Flower seedlings

Basil tastes like basil from the day it sprouts, so if you do have to thin, make a salad!