Don’t know of this working this way. The incoming connection needs to connect to a device to find out what the domain was resolved. I think it’s easier to forward different ports to different machines.

Example: domain.com resolves to your IP. Port 80 forwards to web/80 on server 0. Port 180 forwards to web/80 on server 1. Port 280 forwards to web/80 on server 2.

Almost all commodity hardware will support this set up.