[Sephiroth]

I am trying to do a reductio ad absurdum.

Are you certain that the AP is not doing a wireless bridge with the Asus? There is a mode on many routers that allows this.

It is almost as if it were half-duplexing.

If you have got the patience, you may wish to put the Archer as the main router having turned DHCP on and see what the wireless does then. Both near the Archer and a room away at 5Ghz.