I might be reading it incorrectly, but for me, Akkad has 16 culture now. So it's borders popped before (or technically right at the beginning of) last turn.
So it could have worked on the ivory last turn already.
It appears you're right about this. I was basing my info on the screenshot for AH completion from the start of the turn which showed the messages for Akkad's border expanding. However, on closer inspection, it appears that they're leftovers from the previous turn which were slow to clear. So Sisiutil did indeed waste 2 turns.
First of all, he needs the extra worker (actually, I think two workers AND a settler but that's beyond the point) now, not at some later point. If he builds it now, by the time it's finished, the ivory is hooked up.
Second, I don't really understand this 'switch to hammer tiles to avoid growth into unhappiness' concept. Even before the granary (which I think is mandatory and can be micromanaged to be built in 1 turn after pottery is researched) every 2 food he produces effectively means 3 hammers. So what if he grows to size 7 with a happy cap of 4 or 5 as long as he's working nice tiles? (corn is 9 hammers already w/o granary, show me smth with hammers that comes any close to this).
Isn't it better to put the overflow into the worker?
Anyway, what I'd really do is: worker, axe finish (grow), settler, finish with chops and 2-whip, overflow into granary, military, military, military (between the military units a lighthouse might be placed once sailing is complete since it effectively costs only 45 hammers).
I don't agree with your suggestions regarding whipping, as there seems to be some incorrect assumptions (based on my understanding of whip mechanics at least).
You seem to have the impression that an infinite amount of

can be turned into

via the whip. This isn't the case, unless you ignore the implications of stacking whip unhappiness. Whipping for 2 pop every 15 turns limits the amount of

->

. Beyond that the only other way to convert

->

is by building a worker or settler. The conversion rate isn't as favorable for worker/settler building as it is for whipping, but it's still better than working lower yield

tiles.
I'm also not sure where you got the 2

-> 3

conversion ratio for whipping. The best case scenario (without a granary) is whipping a 2 pop city down to 1. That yields 45

, and the city will need 36

to regrow the whipped pop. So a 4

-> 5

ratio. And as the city gets larger the ratio becomes less favorable because the

from each pop stays the same, but the number of

to regrow goes up.
I also think you've underestimated the cost of having the city grow into unhappiness. At that point the unworking citizens are effectively lowering the yield of the high food tiles that your city is working. So 1 unworking citizen means the corn tile drops from a 6

tile to a 4

tile. Two unworking citizens and the corn's only worth 2

, the same as an unimproved grassland tile. The only reason you'd want this to happen is if you needed the extra pop to reach the pop limit needed to whip an expensive building (which isn't the case here).
I agree that it would be helpful to have another worker ASAP, but you have to look at what you'd be giving up to prioritize it. Because whipping is going to be so important with this high food capital, and the limiting factor for how much whipping you can do is the whip unhappiness I would think you'd want to whip ASAP so that the unhappiness can start cooling down so you can whip again sooner. Delaying the initial whip for several turns to build a worker doesn't seem optimal. The fact that the worker build can be used during the whip unhappiness period to stagnate growth while still working the highest yield tiles is another advantage of waiting.
I wouldn't put the whip overflow into the worker, or just whip the worker for that matter, because in this high food case the key is maximizing

->

conversion. Since a worker build does that directly I would choose that option, so that all of the whip

can go to units (which can't be built directly with

).
Granaries would pay off in the long run, but it takes a few whipping cycles for that to happen, and I think Sisiutil is going to need to launch his attack before that, so granary builds will only slow the rush down.