I think I have a similar set up, but no Google WiFi mesh.
When our daughter was born I also put in an IP camera... My FiOS WiFi couldn't handle everything I had going on, let alone the range was not great...
I ended up disabling the FiOS WiFi access point and getting 2 Ubiquiti (UniFi) access points. It works really well. When I move around the house, or even go into the yard (outdoor access point), I never lose connectivity. I can stream a movie and move between each AP.
The issue here is that the main Puck is a router. Wireless clients end up getting an IP address from the Google subnet (whatever it uses). FiOS uses 192.168.1.x/24 network. It isn't a good idea to have both the FiOS and Google using the same local IP subnet, since they're both routers, as you can see it creates problems.
Because of how IP subnets work, I would do one of the following:
1. Set the Google Puck to 'Bridged' mode or look at getting a true AP (not a wireless router). Putting the Puck into Bridge mode will not let you use the additional pucks for the mesh (https://support.google.com/wifi/answ..._topic=6246470
2. Go for an access point. An AP uses your existing network IP router. They generally only have 1 port, which would plug into your FiOS router, or any other network switch. You would only have 1 IP subnet now, instead of 2.
3. Enable the FiOS WiFi for phones/tablets that will be streaming.
As for the speed issues, Mesh networks aren't the greatest. Each puck communicates wirelessly with the main puck. So if you don't have a great connection between the pucks, there will be latency there, not to mention the standard latency from wifi in general.
Are you able to move the pucks closer together? If they're on different floors, that would cause more of an issue as the signal now has to pass through structural obstacles.
If it were me (and it was), I'd go for option 2 above.
Here is how I have my set up.
My Fios Modem/Router is in my living room. I have my AVR, HTPC and Apple TV 4K connected to it, in addition to a switch in my basement.
The switch in the basement has my access points plugged into it. The APs run to different parts of my house + yard.
I hope this helps!