G34 has 1.2Gbps speed compatibility with Xfinity so the speed plan you are in is the right one. But it depends on the location speed differs so just reconfirm with your ISP about the compatible speed for this particular model and You can try changing WIFI channel.  If other Wi-Fi sources such as neighboring wireless access points are using the same wireless channel, this may cause intermittent connectivity issue slow speed, even if the competing signal is relatively weak.  Changing the wireless channel within the  gateway can improve connectivity and speed.

http://arris.force.com/consumers/articles/General_FAQs/G34-G36-Changing-the-Wi-Fi-Channel

The “up to 3000mbps:” speeds aren’t reasonable. They’re adding the 2.4ghz and the 5ghz. And its at optimal levels at that. Arris isn’t good at saying if their routers are 160/80hz or how many antennas they have internally. So the G34 could be a 4x4 antenna device with 80hz wide channels or a 2x2 device with 160hz wide channels to get the 2400mpbs 5ghz link. Meaning, if your device you’re testing with is only 80hz capable and the router is 160hz 2x2, its max link speed might be only 1200mbps for your phone. Or if you’re phone only has 1x1 antenna, it might be a 600mbps link speed. And thats link speed. Actual throughput tends to be around 55-65% of link speed. Plus there’s interference, device efficiencies, etc that can all slow speeds or have lower link speeds. That might be why the spectrum person said you can only expect around 500mbps out of the wireless on it. Tough to know really without knowing exactly what device you have, how you’re testing, etc. 

You should be able to get your full 800mbps out of a hardwired connection.

If you’re curious about overblown wifi “up to***” speeds, check out duckware. His site dispels a lot of misunderstandings about wifi and actual speeds. It can be a long read though once you enter that rabbit hole.