Hi,
We should be pretty close to you as the lake is a little under 2 hrs from the portal and we will start between 1:30 and 2:00 am.
Your 12 hrs from the lake to summit and back down is probably not too far off, maybe an hour or so short unless your team is pretty fit.
Having spoken to my girlfriend about Kili and her having now had a practice on the lower parts of Whitney she says very much different.
Whitney is, from the Portal to summit and back, around 13,000 ft of altitude change and also what can be a 60 degree temperature change, all within 14 to 16 hrs.
I am by no means an expert on these types of hikes but last year it took me 12 hrs and I thought I was in pretty good shape for an old man.
Beers are on me, as you would expect from a Brit, at the bottom !!