For now I think we just look at traffic over each interface, don't worry about qos tagging and priority etc, just how much traffic flows over each interface during your "lockout" period. that will tell us something about where the traffic is going and hence where the problem is.
When you run the fireqos test, it puts all that stuff to your screen. And that comes after the line resetting the firewall, so it's apparently not the firewall locking you out. So evidently you can receive data from the router. But when you try to access the router, the router doesn't respond. That seems strange...
Suppose you create a new connection to the router to see LuCI page... packet comes in eth0.1 headed for 192.168.1.1 hits the bridge, and is delivered to the router at br-lan 192.168.1.1 the router then tries to send response... packet is sent from 192.168.1.1 via br-lan, the bridge looks up your mac address and sees it's on eth0.1 and sends it... I don't see why you should be locked out. So the fact you are locked out is what we need to figure out.
EDIT: if you are right that router can send you information, then it might work to connect to netdata and watch it, then in separate ssh window run the test, and watch netdata dashboard while you try to surf and do whatever. see which interfaces have traffic, how much traffic, etc. Is there some big spike in traffic over certain interfaces? Does something saturate the router with packets in a loop? Does something else strange happen? Lots of packets over pppoe-wan but no packets over br-lan.
Even if you are locked out of netdata during that period, when router comes back you should be able to see what happened during lockout.