UPDATE:

After completing day 5 of my egg fast, I bounced back up 1/2 lb. So my final weights looked like this:

Started egg fast on Friday 11/7 with a starting weight of: 261.4 lb
end day1: 260.0 lbs (1,790 kcals -- 84%f / 0%c / 16%p)
end day2: 258.1 lbs (1,915 kcals -- 83%f / 1%c / 16%p)
end day3: 258.8 lbs (2,266 kcals -- 81%f / 3%c / 16%p)
end day4: 257.3 lbs (1,553 kcals -- 84%f / 0%c / 16%p)
end day5: 257.8 lbs (1,915 kcals -- 85%f / 0%c / 15%p)

NOTE: the carbs came exclusively from cream cheese

Total lost: 3.6 lbs

After the 5 days of egg fast (incidentally I agree with deansdad, it bothers me that it is called a "fast", when a fast really means not eating anything, but I digress), so, like I was saying, after 5 days of egg fast I was supposed to do 2 days of "weaning" where 1-2 of my meals are still egg-fast, but the other meals are my "normal" keto diet. Unfortunately I made a mistake, and left my breakfast and lunch on the counter before heading out into the back country for the day. So my first day of weaning ended up being a 24 hour fast. Then I threw caution into the wind on my second weaning day, and just ate what a I wanted (all keto of course)

end day 6: 257.1 lbs (1,111 kcals -- 67%f / 9%c / 24%p)
end day 7: 258.9 lbs (1,800 kcals -- 71%f / 3%c / 26%p)

So I regained 1.1 lbs 2 days after the egg fast had finished. Making my "actual" weight loss 2.5 lbs for the egg fast.

So for me at least, the egg fast seemed to help in breaking the plateau/stall. Incidentally, today (day 8), my weight dropped to 256.6 (on 2,091 kcals) brining total weight lost since starting to 4.8 lbs. I must admit, it is very nice to see the scale moving again after a month of bouncing up and down +/- 2 lbs.

If I remember, I will try to do one last update in a week or two, to report if the stall is actually broken long term.