well what you want is theoretically possible.
there are some burdens like named virtual hosts and wrong listeing ports and execution time limits but you could theoretically follow the specs and do everything in php. you can open sockets and write raw data to it so theoretically anything is possible.
but its totally absurd and senseless.
however your problem is not new and there are solutions for that.
they are called propagating cdns.
most of them provide edgecasting for delivering content with high speed and low latency (this is the usual use case), but you can also use them to balance traffic.
most cdns of coruse cost money.
but there is a project devoted to this very specific problem. to cache content and deliver it for low bandwidth sites and only fetch it from there.
its called the coral cdn, you should check it out. the probably most used commercial ones are akamai, cachefly, and level3.
