Accessing via 127.0.0.1 via home network
You cannot with just ordinary TCP/IP let other computers access your web site on the Mac Pro using the IP address 127.0.0.1. This address has a special meaning in the IP protocol, and always refers to the local computer - never other computers.

If you really want to do so, you'll need to use port forwarding. You can use SSH to port forward the remote port 80 to the local port 80, and thus be able to access the remote AMPPS web site using the 127.0.0.1 address.

However, there's really no point in doing so. It won't make it faster, better or anything else. As you write no reason for wanting 127.0.0.1 specifically, it seems you're better off using an ordinary RFC1918 IP network on your home network - such as for example 10.x.y.z/8 or 192.168.x.y/16.