@Imroberta, welcome to NGA. I'm not very active here any longer, but your question was referred to me. I've grown seedlings by the many 100's.
First, ignore, totally ignore those who tell you that your seedlings should confirm to some sort of shape or size. They don't know what they are talking about. Every single seedling will be unique, even those from the same seed-pod.
I transplant my seedlings from a "community pot" to their own 4" pot when the seedlings are about 4" tall. I think that your seedlings now need to be in their own pots. When they are twice that size, move them into gallon pots. My seedlings have always grown outside. I'm in Vero Beach, FL, and though our summers aren't as hot and certainly not as dry as your climate in AZ is, I've never worried about heat. I will allow my seedlings to get a few hours of early morning sun and/or a couple of hours of very late afternoon sun, but from about 10:00 AM till 4:00 PM, they are shaded. I had a lot of plumeria in-ground, and having these large-leafed small trees, the seedlings did very well underneath them. Any sort of fairly well-leafed tree will do. If you don't have this, how about a porch that might get only a few hours of early or late sun? I'm sure you've got somewhere to put these few plants. You should plan on watering your seedlings every day or two. That sort of depends on the amount of sun, the temperature, and how low your humidity is. Our humidity averages above 80% all year long, and that helps these tropical trees endure heat. You won't have this option, so anything that you can do to increase the humidity around the seedlings, the better.