Tangs "most of the time do OK with each other if you add at the same time and they are young/smallish when you add them. Since it sounds like you really like tangs, consider doing a species tank. Some tangs will do well if you add 3 or more of the same species.
Consider adding 3 banner fish with a flowing fin they school and look really good with tangs. A nice school of green chromis, adds green color to the tank. :happyfish
Numbers of fish to the gal, can be a tricky thing. You can stock two ways first stock the tank based on what size the fish will be or stock based on the current size. I run home made systems on my tanks, so I have 75 gal of water in the filter setup to 125 gal of tank. If you have this, the tank is stable enough to "pack" the fish a bit more closely. If you have 5 gal's water in your filter system the fish numbers are lower. Also I will stock a tank with juveniles, knowing that in a couple of years, some of the fish will need to be moved as they grow, not because they are to large for the tank, but but because they are to large in the numbers of fish inch to the gal. But only do this if you are planing to add more tanks. :happyfish
If I wanted to "pack" the tank and it sounds like that is where you are leaning, this is what I would do.
Set up the system around a large under tank, a big plastic tub from wall mart or 75 gal tank with a wet dry drip and protein skimmer at each end. The center where the return water comes from I make into a refugium. Set this up and cycle for a few weeks,with stuff and critters in your refugum.Add your clean up crue cycle another few weeks, Add your 7 green chromis, cycle another few weeks, add the 3 banner fish cycle another few weeks, when the tank is 6 mo old and totally stable (this is very important because by adding groups of fish, you strain the system.)Add the Tangs 3 to 7 I would include a yellow because they show off the other colors in the tank. Some tangs grow fairly large. be prepared to move some fish latter.( in a couple of years).