Yep. I checked it in Orgrimmar solo and with shaman totem and BL. I have 709 haste rating (21.6%) with spellstone. Plus totem,BL and BD and incinerate cast time = 0.949 sec.
Counting:
New Cast Time = (2.25*0.7)/(1.216*1.05*1.3) = 0.949 sec. As i see, you are right in backdraft multiplier.
So, then
For incinerate when +BackDraft on.
1 sec = 2.25сек*0.7/(1+X/100)*1.03*1.05*1.3
X = (2.25sec*0.7)/(1sec*1.406)-1 = 0.12 or 12.0% haste = only 394 haste rating.

Did you read the patchnotes? You can't throw on UA and immo anymore at the same time.

According to the Warlock DPS spreedsheet with my gear loaded in to it, immolate is still worth casting in 3.0.8 for me.

Since 3.1, with the UA/immolate change, hasn't been released and I can still have both UA and immolate on the same target, I'll continue to use both until it is changed on the live server.

I don't believe anyone ever doubted that Immo was worth keeping up since 3.0, I can't think of a spread sheet anywhere that showed otherwise. Most of the current discussion is for the upcoming changes (3.1 and later), which is where Immo and UA will not be able to be kept up together. The Immo/UA change HAS gone through onto the PTR so most are accepting this as no longer debated, but an incoming change.

Well... on my character it does anywhere between 1k and 1.3k currently. So if they axe 30% of that it should still be at 900 tops. That's still way better than whatever standard pet affliction can come up with.

The doomguard on live does 2.84 times as much damage per (average) melee swing as the succubus. On the PTR this number is 1.89. If you want to be exact, it's a 33.51% damage nerf for the doomguard, but it's still better than the succubus. (Not quite 1.89 times better though, since the succubus gets lash of pain in addition to melee swings.) Simulationcraft for 3.1 shows the doomguard to be about a 300 DPS increase over the succubus.

Would you mind running the spreadsheet again using the latest numbers from 3.1 sim tests?
Warlock_T8_53_00_18 intellect=0.19 spirit=0.77 spell_power=1.54 hit_rating=1.91 crit_rating=0.74 haste_rating=0.96
I'm curious to find out how this will influence your perfect set.

Makes total sense. The same thing happens with curses: the last one casted will overwrite the one already on the target. Otherwise you could never replace a CoA with CoE.
Did you also try it the other way around, overwriting Immo with UA?

New to warlocks, I've read up on all the TC but I was hoping to get some clarification on this:

At what point is it no longer worth it to cast or refresh dots? Say a boss is going to die in 10-15 seconds and dots are not going to get their full duration, which ones are still worth reapplying? At what exact time to kill do the various dots become worse than the filler dps-wise?

Or to pose the same question but in a different way, say you need to do the highest burst damage possible in 10 seconds and no dots are up, what to cast and in what order?

Assuming deep affliction obviously. (I'm also interested in how this might change after 3.1)

This is what I use:

CoA: 12 seconds
SL: 12 seconds
UA: 9 seconds
Immo: 9 seconds
Corr: 9 seconds

Disclaimer: I've only used simple DPCT math to get those numbers, so I'm not sure they're perfect.

I assume your question is specific to Kologarn. I suggest not reapplying any dots at all when Stone Grip hits, and just shadowbolting.

It's not just for Kologarn, it's fairly general, I was thinking of all fights where you need to switch target and burn down something quickly, or when a boss is at 2% and all dots are falling off, most of the TC assumes max dot duration so it was a bit of a gray area.

Your list doesn't mention Haunt, it's not a dot but it's still assumed to be up. Is it always first priority?