Auto starting and stopping docker-proxy.exe per running Windows container.
Keep this running and it will start a docker-proxy.exe process for each running or started Windows container with published ports.
It will also stop the process again when the container is no longer running.
You can now request http://localhost:8001 on a Windows container started with -p 8001:80
From Windows NAT (WinNAT) — Capabilities and limitations
Cannot access externally mapped NAT endpoint IP/ ports directly from host – must use internal IP / ports assigned to endpoints
Hopfully this will be resolved "soon" according to microsoft/aspnet-docker#13 (comment) but until then...