Lets try this. If you still have the FiOS G1100 set up and acting as a primary router, disable the ASUS router as well as the Deco nodes and see what your speeds are while connected to the G1100's Wi-Fi. It is a 3x3 802.11ac Wireless router and on many devices, you should expect approximately 300Mbps out of it. You can achieve a full 600Mbps on a clean environment with it as well with a 2x2 802.11ac wireless device. A 1x1 802.11ac device will max at 300Mbps, usually achieve around 180Mbps. A 3x3 Wireless device can get up to 850Mbps, usually averaging around 500Mbps.
The trick here is, you'll want to make sure the Deco nodes are hardwired to each other whenever possible using Ethernet, even if they tout a dedicated wireless uplink. Wired backhaul is not only more consistent but it allows for the units to operate on independent wireless channels instead of colliding onto the same channel (programming dependent - not all mesh systems do this.). You'll also want to make sure Wireless on the G1100 and your old ASUS router (if still plugged in) is disabled so they're not adding to any wireless congestion which may exist.
Another thing to pay attention to is whether or not your wireless devices are joining a 5Ghz signal or a 2.4Ghz signal. 2.4Ghz will typically be slower (although a stronger signal) compared to 5Ghz. If your network names are combined, Deco will usually attempt to steer your devices to 5Ghz as well as to the nearest AP by default but, at the end of the day, it is up to your device to make the correct decision. Many devices aren't the smartest, and tend to choose 2.4Ghz because the signal is stronger or, because they believe battery savings will be had, when 5Ghz may be the actual, better choice. Or they may choose a further away AP because it sent a beacon first while the device was scanning for nearby wireless networks to join. The best way to "steer" a device is to feed it a weaker signal - Turn down the 2.4Ghz transmit power, while keeping 5Ghz high so they are equal in coverage.
For the Authentication issue, this may boil down to Band Steering, AP Steering or Fast Roaming settings on the Deco. Although I'm not familiar with the product, see if it allows you to toggle off these features and see if stability improves. If it does, turn them back on one at a time and see which one is breaking your connectivity.