Hi there Michael, I will try to assist as much as I can. The short answer would be to keep practicing the 'spider-web' warmup. Stretching your fingers and being able to reach comes with time. Some chord shapes can be rather difficult and 'stretchy,' but they become easier the more you practice them. As for your wrist, you definitely want to watch out for any soreness. Create good habits with the physical aspects of guitar playing. It sounds like your wrist might be curling too much. Try angling the neck higher, you could also rest the body of your guitar on your left leg instead of your right. Try that, while stepping your left foot onto a block, or the leg of your chair, effectively raising your guitar neck hand position.

Try these things, see if they work for you!