NAT/forwarding issues while gaming/streaming

But... are those ports truly opening for full peer-to-peer traffic?  As in, can unsolicited inbound traffic get through?

That is the true root of the problem... not just whether UPnP or manual port forwarding can be setup locally on the router.  There needs to be the ability to have unsolicited inbound traffic from the edge of their network all the way to and through your modem.

As in, if you were to use port probing tools at the likes of speedguide.net or grc.com's shields up! tests and verify supposedly open ports are actually open to your forward facing IPv4 address.

To date, their network topology above the modems has been breaking such peering traffic, regardless of whether our local routers appeared to be opening ports locally.  Sure, consoles and the like may report less restrictive NAT and such... but when the truly unsolicited peering traffic needs to come in, things still failed to work properly.