What you want to do is create one SSID for your house, and let your devices roam between access points without having to reset their connections.
To do this:
About #3. This means making sure the only router with its WAN port connected is the Verizon FIOS modem/router. The other routers providing wifi have an empty WAN port and connect to the FIOS router through their LAN ports. The 'extra' wifi routers all have DHCP disabled. (this is very important.)
Setting the wireless up like this clues your wireless devices in to the fact that these separate wireless bubbles are part of the same network and not part of different networks. Modern devices understand this scenario and know that they don't need to change IP addresses when they hop from one WAP to another. This means they don't drop all of their active connections (like phone-app baby monitors) when they hop to the other WAP. They just stop sending packets to one wifi bubble and start sending them to the other instead.
You will probably still have dropout zones that receive no signal. If you want, you can fill these in with more WAPs configured to the same security settings. The wireless bubbles can overlap, it's fine. Modern devices know how to deal with it.
More complex devices like laptops have settings you can mess with to change when they hop between networks. In Windows, you can access advanced wireless driver settings to tell your device how aggressive it should be about roaming from one WAP to another. More aggressive settings cause it to hop more often, every time it detects a network with an even slightly stronger signal. Less aggressive settings mean if the two are close in signal strength it will stay attached, and only roam when the one it's attached to gets significantly weaker.
If you have difficulties with cell phones, try changing 'automatic' settings into 'fixed' ones. I've set up the exact network I'm describing, but had trouble with a certain setting causing cell phones to be unable to connect to one of the routers. I think it was automatic draft-N mode or something, but this was a while ago. The problem may have been specific to my router, hard to say. (Not my house, just helping them fix it.) The symptoms were that a cell phone would stay connected just fine in one area of the house, but would start disconnecting and reconnecting when it entered the other. If you see that, start changing one setting at a time to find the setting that's giving the phone problems.
Disabling wireless draft-N mode is a problem for wireless bandwidth to devices that support it. The best way to fix this (I think) is to use 5ghz bubbles for devices that need bandwidth like laptops and internet TV gadgets, while using 2.4ghz for roaming devices like phones and tablets.
It can be a tricky setup initially, but after a few days of troubleshooting you'll get it stable and everything will work great. Have done it myself, got all of the iphones and ipads and android phones and laptops in a family holiday party all roaming from one end of the house to the other without a single dropped ping. I mentioned baby monitors because that's what spurred the change. Someone needed a baby monitor cell phone app to keep running no matter where the phone went and which wireless bubble it was in. Separate network SSIDs meant every time the phone switched it would get a new IP address and drop all existing connections, which is no good for anything that's streaming video from another LAN device while you walk around.