As @edg1 said, there's no way to get above the theoretical 500 Mbps with MoCA 2.0, which is all the Quantum router offers. There's a pretty good chart the bottom of this page found at the MoCA Alliance website, that shows what the various MoCA standard support. From that chart, you can see there are MoCA standards that support higher speeds. If you are willing to ignore the MoCA adapter built into the Quantum Gateway Router and buy a pair (or more) of other adapters, you should be able to get near to the speeds you would like.
To get that level of speed from my office downstairs up one floor and to the living room on the opposite side of my house, I used a pair of Actiontec ECB6200s that I bought from Amazon. (I have plenty of coax in the walls, but no Ethernet cables.) They use bonded MoCA 2.0 signaling. While I don't quite get gigabit speeds from them I do get:
in one direction and:
in the other.
How you would use these is to plug one of the Quantum Gateway's gigabit Ethernet LAN ports into one of the ECB6200s. Connect that to the coax (via [wide frequency range] splitter or directly). Then in the other room, connect the coax to the other ECB6200 and then to your computer (or a switch if you need to connect more than one device). If you have Verizon STBs for your TVs, bonded MoCA 2.0 is supposed to be able to coexist peacefully with regular 2.0 on the same coax. That is to say, they should still work (at their 450-500 Mbps rate) while the speed between the Actiontec ECB6200s should stay around twice that. I have not tested that myself though.
As you probably noticed, neither of these supply a wireless signal. If you like boosting your wireless coverage, you would want to get one Actiontec ECB6200 (for use at the Quantum Gateway side) and pair it with the Actiontec WCB6200Q also available at Amazon (for use where the current extender you have is). I've never used the WCB6200Q personally, but it is the appropriate one to use as it supports bonded MoCA 2.0. (As a side note, I believe the Network Extender you get from Verizon is a rebranded Actiontec WEB6000Q.)
Ideally, one would like to get MoCA 2.5 or MoCA 3.0 adapters to get the very last bit of speed from Verizon's (near) gigabit service. However, while the roadmap at the MoCA alliance shows that 2.5 should be out (2017) and 3.0 should out or close (2018), I have not found the adapters for sale. Actiontec offers a MoCA 2.5 adapter, but only to "Service Providers ONLY."
My setup: 75/75 Mbps; Linux router (2x 1Gbps ports) + iptables; Netgear Orbi x 2