How do I Book a Cairo Trip with 2 Long Layovers Without It Costing My Soul?

Planning a trip from the DC area to Cairo for 6-7 days around late December/early January and trying to figure out the best way to do two long layovers/stopovers, one on the way there and one on the way back. Three if we can get it to work and not cost a fortune. Or if you have a forth rec to replace London?

Ideal would be something like:

DC → Paris/London/Casablanca → Cairo

Cairo → a different one of those cities → DC

We would want around 10 to 24 hours in each stopover so we can actually leave the airport and explore a bit.

Has anyone done something similar? Did you book it yourself as a multi-city ticket, use separate one-way tickets, or go through a travel agent? Was it much more expensive?

Also curious which combo people would recommend between Paris, London, and Casablanca. Paris seems great for sightseeing, London seems easiest, and Casablanca seems like it could be cheaper.

Would love any airline, route, or booking site recommendations that worked well for this kind of trip.