The only recommendation I would give you, is do it again. Egypt is considered by many to be the most time considerate settlement, with many people having 10 or more days left when they finish. Whatever the issue was that caused you to complete it with so little time remaining (for the bonus building fragments building ONLY - you get the main building award no matter how long you take to complete) - will most likely be the same issue on any other settlement.
Whatever you think you might have done wrong, or what you think you can do to improve the time you spend doing the settlement is best served by doing it again (and when you complete the 2nd time, you will get an emmissary to use in your Town Hall) and you will hopefully find ways to improve your method.
Myself, personally I am working on my 4th Egypt. Boring as hell, but the final prize at the end of the tunnel is a valuable addition to your city.
People may tell you that Japan or Vikings is quicker to do - and truth is, yes it is - but, you also have much less time available to complete, if you have a goal to obtain the fragments for the secondary building.
If you can figure out what you need to do to hasten your Egypt settlement, that will probably be very much what you will need to do to complete other settlements at a quicker pace.