In 12GCDs, TTT4 x3 > TTT x4

150 + 200 + 360 = 710 * 4 = 2840
150 + 200 + 360 + 290 = 1000 * 3 = 3000

12 * 2.4 = 28.8

2840 / 28.8 = 98.61111111111111
3000 / 28.8 = 104.1666666666667

That's hitting all positionals. Hitting only 1/2 of your positionals (we can average this down to 245 Potency per 4th)

150 + 200 + 360 + 245 = 955 * 3 = 2865 / 28.8 = 99.47916666666667.

So hitting 50% of your positionals is only a 0.8 PPS increase over TTT, so yes, keeping BotD up is crucial. But as I said, it's all situational.

In 6 GCDs:

TTT X2 = 150 + 200 + 360 = 1420
TTT4 TT = 150 + 200 + 360 + 290 + 150 + 200 = 1350
ID TTT4 = 180 + 200 + ((150 + 200 + 360 + 290)*1.1) = 1480

So if your Target is alive for 6GCDs, then ID TTT4 is the quickest way, hands down, to burn it down.

For 7 GCDs:
4*2.4 = 9.6 / 3 = 3.2
IDC TTT4 = 180 + 200 + ((250 + 150 + 200 + 360 + 290)*1.1) + (35 * 3.2) = 1867
TTT TTT4 = ((150 + 200 + 360) * 2) +290 = 1710
ID TTT4 T = 180 + 200 + ((150+200+360+290 + 150)*1.1) = 1645

So in 7 GCDs, IDC TTT4 is best.

But, none of this really, takes into consideration BOTD uptime nor Geirskogul. IDC TTT4 is risky and limits a lot of Geirskogul use.