Hi there!
I like your set up with the plant rack :)

Funny, I was just repotting my basil, it grows like a monster even in the heat wave we've been having. So I was just stumbling through some basil info.

I'm certainly no expert so I'm sure others will have more/better advice for you, but from the looks of it, it seems like you have quite a lot of basil plants in one pot. Each one needs a lot of room to itself (I've heard 6" apart is good spacing?) which means right now your basil plants are all competing for water, nutrients, sunlight, etc. I think that's probably the reason they aren't branching out much and only growing up. I'd guess thinning them out or moving them into separate pots would help, but again I'm pretty much a newbie with plants :P

Question: are you using your garden soil in the pots?

I am using moisture control potting mix because I have a tendency to over/under water. Also have a miracle-grow fertilizer pellet/stick in there.

Also, here are some close ups as promised:

Consensus seems to be too many in each pot. Would 4 in the large and 2 in the other be ok OR is that still too crowded...

I agree with sykeros, they look crowded but healthy :)
Also, I'm just wondering but are you plucking leaves from the top of the plant or down the stems?

Here is what everything looks like after I moved stuff around...will they be ok (at least for a while) like this? I really don't have room for more pots....

these have 3-3-1 stems respectively

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these have 2-3-2 stems respectively

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all together everyone say (mozzerella) cheese!

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That's much better :)

Be careful with Miracle Gro Moisture Control potting soil. I find it doesn't drain well at all. I rotted out almost my entire greenhouse two winters ago. It really holds water. I even lost fuchsias and they love water.

Pinch or cut out the growing tips rather than picking off individual leaves. That will cause the plant to branch out from the remaining nodes. Keep doing that as each branch grows. It will also inhibit flowering for a while longer, letting you get more leaves before the plant flowers, which causes its flavor to suffer.