Egg a day sounds like it has calcium in it. To much of that when they are young can cause kidney failure.
What about grower feed? I don't know but wouldn't that work? Then you would already have a bag when it was time to give it to them, that is if that have that on hand.
I hear they like yogurt, and that would probably be good for them. Many people suggest giving this to them when they are sick, so why not when they are healthy?
When my chicks were young I would go out and find them some(5 or less bugs for the 3 of them) bugs nearly every day, it was really entertaining to watch and they loved it. Plus it was a great motivator to get rid of the grub problem I had, one at a time! lol!
Mine LOVE bird seed, I give them a handful almost daily still. I did not give them any till they were outside but I don't see why you couldn't fill the time gap with some of that as well, just might have to break up some of the corn and sunflower pieces for them. Plus you can get a pound for $1 or less around here. I have not bought any scratch yet because I have so much bird seed from back when I bought a bunch to feed the wild birds. So I don't know which is cheaper and the ingredient differences.
Also I agree with Wildsky's suggestions.
Maybe even look at the ingredients of the starter and try to come close to it? I wouldn't obsess at trying to match the nutrition, but it couldn't hurt to try while you are waiting for the feed to come in.