The USGs can do Gigabit speeds as long as Smart Queues and IPS/IDS are disabled and the L2 / Hardware Acceleration features are enabled. If any of those features are on, the USG 3P will cap off at 80-120Mbps, and the USG Pro 4 will cap off around 300-400Mbps. They have old MIPS processors and can't push traffic like their newer Dream Machines can, which do all of the routing in software on ARM processors.
The other thing to note is, if OP is running a speed test from the UniFi Controller, even if the USG itself is delivering 1Gbps of traffic, the speed test in the UniFi Controller runs off of the USG. The USG's CPU will bottleneck the speed test at the same speeds you'd expect to see if you didn't have hardware acceleration enabled.
A couple things do come to mind though.
1: Make sure the USG is fully updated. Firmware as far back as two years ago had issues with UDP traffic, and some of those issues also cascaded to TCP Traffic.
2: Turn off MSS Clamping. Not needed on FiOS as long as your network is already at an MTU of 1500 end to end.
3: Make sure Hardware Offload, Layer 2 Blocking Offload, and Offload Scheduler are all enabled.
4: If the USG is configured using Class A blocks on NAT, configure for Class B instead (old bug a while ago caused slow speeds if using Class As in some situations) and see if performance improves.
5: Log into the USG's CLI and run a `show interfaces ethernet detail` and look at each of your Interfaces. Make sure you do not see overrun, errors, or carrier collisions being reported for TX and RX on any interface.
I have a USG 3P on Gigabit DOCSIS and it handles the connection fine. A friend of mine has a Dream Machine Pro on FiOS and gets the full 940/940.