This is fairly untrue about the Hanged Man portion. It's true that you want to wait for 3 SS's to get summon, but your initial rotation should always utilize a Blood Tap.

IT - PS - BS - (blood tap)SS - SS <Gargoyle now>
ERW
DC - SS <or Gargoyle now> - SS - DC - BS - BS

Now for the sake of smoothness, always using the first gargoyle slot isn't a huge loss even if using Hanged Man, though clearly the 2nd would be most optimal due to the fact that you will have all 3 stacks up. And clearly this is specific to using a reaping build.

I think it depends on whether the fight is long enough for 2 gargoyles.

You want one of the gargoyles to have a speed pot. If there's only time for 1 gargoyle, speed pot for that gargoyle. If the fight's long enough to have 2 gargoyles, use the indestructible pot pre-pull, and do a non-speed-pot gargoyle for the first one (since the pot will be on CD). When it's time for the 2nd one, wait for as many AP/haste procs to align as possible, then speed pot + gargoyle, without waiting so long that your gargoyle is still alive at the end of the fight.

It also seems a bit of a waste to me to speed-pot before the pull. The only fight I can think of off the top of my head where you don't have to run in pretty far to start DPS is saurfang. Let's say you have to stand 21+ yards out to avoid aggroing the boss. At a standard 7 yard/sec run speed, you'd spend 3s running in before you can start DPS. Since the haste pot only has a 15s duration, that seems to be a big chunk of wasted pot time.

Good news regarding pet scaling with the ICC buff:

Source: http://worldofraids.com/

Even with the loss of 3 seconds, Potion of Speed comes out ahead, just do the math. Also, the number of gargoyles you summon is irrelevant. Potion of Speed before summoning gargoyle is higher dps than Indestructible Potion before summoning gargoyle. If there is time to summon two gargoyles in the fight, then use two Potions of Speed. One more thing, with the new proposed 0/17/54 spec, Indestructible Potion will be useless for DPS anyways. Right now it's just suboptimal, not totally useless.

Indestructible is a pretty accepted method of pre-pull potting. If you have math that shows it's wrong, then by all means prove it. Until such time as you do then your argument has no validity. I have a feeling you've missed something in this magical math you've done to figure out that speed pot is better.
1) You lose at least 4 seconds of DPS time with speed pot while poping Army pre pull.
2) You lose at least 3 additional seconds of DPS time running to the boss.
3) You now have AT BEST 8 seconds to pop gargoyle or lose the speed pot boost on your cast. Your raid isn't always going to be ready for Blood Lust inside that 8 seconds, so now you are faced with the choice of wasting your speed pot or not waiting for BL to pop your first gargoyle.

Seems to me to be a pretty clear cut victory for Indestructible Potion pre-pull. For about 1m53s all your attacks and your Army and your Gargoyle benefit from using an Indestructible pot, the same can't be said of a speed pot.
Of course 0/17/54 changes everything. You will be using Speed Pot x2 once you're spec'd that way, but until then I see no logical way around using Indestructible.

I think he was talking about using army, then speed pot, then running in, so that's 4 seconds extra army time.

OTOH, if you want to Sigil of the Hanged Man buff to be up when you pop gargoyle, you need time for 3 scourge strikes. Even if you used the speed pot immediately before the pull, you wouldn't have time to get them in before the speed pot buff fell off. Even if you're using the Sigil of Virulence, it'll be tight, since you want to put up frost fever and blood plague and get desolation up before you hit that first SS.

IMO if what's on the PTR goes live and frost becomes the best subspec, it will be interesting to see if there's a reliable way to get a gargoyle up within the first few seconds of the fight with both bloodlust/heroism and the speed pot haste.

Did you even read the whole post? I said cast AoTD and then potion of speed. The only lost time is 3 seconds running to the boss. Thus, you only get 12 seconds of the speed potion. In terms of EP values:

97 ap for 2 min. is basically 97 EP averaged out in those 2 min.
500 haste for 12 seconds is (500*1.95*0.1) = 97.5 EP

97.5 > 97. 1.95 was the value of haste, and the 0.1 is referring to the average time it was up in the 2 min. As in, 12 seconds/120 seconds. The difference between the two is 0.5 and thus, they are essentially the same. However, you need to take into account the fact that if you pre-pot Potion of Speed instead of Indestructible Potion, your gargoyle will get the 500 haste instead of the 97 AP. This is a larger gain in DPS than losing 4 seconds of army time.

This will be moot shortly anyhow if frost subspec turns out to be higher dps. No bladed armor means armor pot is useless.

Would this affect gargoyles and army of the dead as well?

They are guardians (like Blood Worms) so I doubt it.

Pet and gargoyle failed the heroic 'Permafrost' achievment in pit of saron a few weeks ago, too.

I dont know if it has been fixed.