pace5268 and uverse tv with velop mesh network

I am having the same problem as well. I have the 5268 because I need the coax connection for my STBs (for now - probably could get the "wireless" if needed), both on first floor and third floor of my home. My house is prewired with coax to a few different rooms for cable boxes and has ethernet runs to about 6 different spots in the house, all coming from a metal can in laundry room.

My main issue comes from my Velop mesh system (house is 4200 sqft total on 3 levels) that will only put out about 100 up/down on wifi when I've got gig fiber in my home. I have DMZ+ enabled and that helped at first... increased my speed from about 30 up/down to where it is now. 

My current setup is 5286 ethernet--> velop on third floor --> wireless connection to 2nd floor node and 1st floor node

5286 coax --> splitter to 1st floor STB and 3rd floor STB (these are the only tvs I have so no issue there) 

I have the bgw210 in possession and can on my own, get an ethernet cable to the STB on the first floor from the current gateways location to be able to switch to the bgw. My question comes here; since I currently have an ethernet cable run to 3rd floor (where I'm connected to main node), can I run one port from on the back of the bgw to the first floor STB, 1 port on bgw to a switch on third floor, then 1 port from switch to STB on 3rd floor, 1 port on switch to main velop node?

bgw eth port 1 --> STB first floor

bgw eth port 2 --> switch on 3rd floor

switch on 3rd floor port 1 --> STB on 3rd floor

switch on 3rd floor port 2 --> velop main node

From what I've read, I need to enable IP passthrough on the bgw to let the velop handle all the firewall and filtering and whatnot. Does this setup I want to go with still allow the TV stuff to work? Ive seen some posts that seem to suggest otherwise.

Also, does the ethernet connection on the back of the STB allow me to get full TV capabilities or does that take out the ability to use DVR?