The corporation you are working within as a sub-contractor has a "huge" ISP. Within every building there are numerous switches, providing ports to each work station, where each computer is physically connected via an ethernet cable. Those working on a wireless computer have been provided with the wireless network connection "code" or the wireless devices have been configured by IT.
Thus, my thought is actually kind of "simple" in the huge scale of this company. When I say purchase your own server, it is indeed your own mini "network center" for your team to connect through. All of your team members computers have their drive mapped to your sever. The server has it's on OS..and it would need "one port" in this corporation's configuration for you to connect your server. Once your team's computers are mapped to your personal server, you would not be accessing on a computer-to-computer basis any "direct" network corporate connection.
In essence, my thought is that you would negotiate with the Director of IT and the Director of the Network team, access to this one port that your sever would connect to, gaining access to their "huge" ISP..The rules of permission as to how much of the ISP network you would ever be able to access would be set up in the network control center. Next you would get your own router, connected to the server. It could be a wireless router that only your team connects through. Or, you configure your sever, connected to the one port, and have all team members report to that room where they are connected to a router switch via ethernet..you can use more than one switch on one router.
I'm sure that the corporation you are working with "worries" that if you connect any of your computers to their ISP network, you "might" gain access to accounts, hard drives and information that is propritory.
A server is not that expensive; you might be able to establish a "lease on the port" and agree to narrow permissions. With that said, only the Internet and software that you install is accessed on your server by your team. With the correct permissions set in place, you would not have any access at all to their corporate computer network.
Think about a huge library, which allows "anyone" to access their wireless network! It's not a "trust the libray user" issue that allows this succes and access, it's a pure and simple network configuration that only allows an individual to access the "Internet" to get on line per precise software and permissions. There is no way in a library (for example) a user can gain access to any of the control panel, system, etc. and so forth.
To infinity this corporation will continue to say NO to you ever gaining access to their network. Instead, offer out this alternative idea?
Just a thought? There always wax to clear out of my ears if my approach needs to be blown!
Continued tenacity with this issue!