While he's correct that one radio is dedicated to mesh communication, what that means is that your device only ever gets 2 streams - which peaks out at 867mbps real world, just like the eero, though I'd be shocked if you got that sort of real world performance.
Though Linksys is correct...
The 330MBPS is likely a limit of the hardware. The eero is a 2x2 AP, which theoretically peaks at 867mbps if you set your channel width to 80MHz. Some of that airtime is being used by the mesh, so i'd say you'd more likely to have a 1x1 max of 433mbps unless you can manually adjust channel width...
I do this stuff for a living, so if you send me your floorplan as an image or PDF, I have all the software/tools to run a predictive analysis of how many AP's you'll need to reach those data rates. It will also show where to put them.
I would suggest you don't necessarily have to get to every area of the house, just 2-3 locations.
If you have access to the attic or basement, you should be able to run ethernet to locations that give sufficient coverage. Then you can overlap your AP's so that each covers a portion of the home...
I hate to be the bearer of bad news, but there is no mesh system on the planet capable of delivering a consistent 500+Mbps rate. The radio technology isn't there. Your only option is to use hardwired 802.11AC AP's set at max channel-width to optimize performance. Even at work where I use the...
My day job is in network engineering, so I'm going to nerd out a bit here - apologies.
Technically, a wireless network is only a mesh network when the various access points use antennas to backhaul their traffic wirelessly to another AP, instead of over an ethernet cable.
Mesh can be very good...