Gaucho - how about an option that goes halfway between a full package and a complete DIY trip. For Egypt, lock down your dates, flights, and hotels, with a TA or a tour group to include maybe one or two side trips to the locations you know you will want to see (Giza, etc). Leave some open days and at your hotel, be nice to the concierge, and get him to find 2 cabs with English speaking drivers, and just hire them on a daily basis. This gives you a bit of structure, but enough flexibility to change plans if you need to. You can also split the group up for a day (or part of a day) if you need a break. The drivers can save you time/haggling/money at some of the tourist spots and markets.

I've done this in the past in Egypt, and in other places. Never regretted it yet, but the max number of people in our group has been 4.