Seeing posts like this make me wonder where people get the idea that using a router as an AP is a good idea. Is it the "mesh" made stupid simple? Is it all of the propaganda touting Asus? I don't get it.
If you have a 9K sq ft house you can probably afford to do this correctly as
@sfx2000 pointed out.
Wire Ethernet to each room and probably at least 2 drops per outlet if you need to switch the cable at a later date due to it not working you don't have to pull another cable later on at a higher cost.
2 AP's for each 3600 sq ft should cover those floors and a single on the 1800 sq ft should work fine as well.
I have an AX AP covering 1300sq ft corner to corner w/ 5ghz and they're only $150/ea - 5X = $750
They work via POE which means they don't need to be located near an outlet like the router as an AP meaning they get powered by the cable plugged into the backside.
Most AP's can be controlled from a Web GUI independently or you can get controller based options if you want to spend more money which shouldn't be an issue if you're spending $2K on routers.
If you want to aggregate the AP's into a single GUI it's an add on ~$150/ea and that bumps your TCO to $1500 + POE Switch + cabling
I would probably stick one of these on each floor to make it simple to drop 2 Ethernet connections down to the main connection point where you decide to aggregate all of the network equipment.
https://www.amazon.com/dp/B08XWKF55C/?tag=snbforums-20 $170/ea POE Switch / 8 ports
So, with 2 switches you're at $1820 or 3 switches ~$2K which is where you were with all the routers but, this setup gets your WIFI clients 1.3-1.5gbps and 2.5GE to wired clients and then you just need an actual router to connect to the ISP
Take off the converged management and you're down to ~$1250 + router / cabling and much happier with performance and stability of your WLAN / LAN.