If you are both on the same subnet, you do NOT have to have the same default gateway. Your default gateway is used for traffic LEAVING your own subnet. Everything else is handled at layer 2 by arp.
So, in essence, you could plug a piece of cat 5 in to a switchport on your router, the other end goes in his. You disable DHCP on BOTH routers and manually configure address, dns, DFG etc. The only difference will be that your DFG/DNS will be your router/ISP, and his will be his. This will work just fine.
Personally, I would do it with 2 routers at each end. One to terminate your internet connection and the other to handle a "point-to-point" ethernet link. You just need to ensure that the subnets at each end do not clash.
Then you plug the second routers switchport into your primary router switchport, and either set up a static route on the internet router, or add a static router in windows to point via the ethernet link router when sending traffic to your neighbour.
There is no simple way to explain this haha