Welcome! Having good drainage for your coop and run is essential; yours sounds good, just be sure. Adding sand or gravel to a low spot will help with drainage if it's going to be a problem.
Have a roof over your run will be a terrific improvement, when you can do it. No rain, no snow (do you get snow?), no standing water.
Scooping poo daily sounds like a miserable exercise to me, even with only four birds. That sand will smell anyway eventually, and then be miserable to remove. And it's not garden mulch! Deep litter, on the other hand, is great entertainment, easy to manage, and transitions to the garden very nicely. I wouldn't use anything else!
Mary