So do you just want wifi repeaters? They never work right at the consumer level.
2900 sq ft spread across 3 floors should not require anything significantly over engineered. Is your house wooden framed or metal?
I have ethernet runs in each room so dropping a unifi WAP in the master, main living and basement covered top to bottom and west to east in my house. However, just the one in the center main floor would cover my house (+5k sq ft) heck, I can even get my wifi at my neighbors.
Everything I have networked is home runned to a central wiring closet in the basement under main staircase. I have two rack rooms for AV and servers for central distribution of HDMI sources and networked storage.
POE is just easier, but frankly, just think of them as plug in WAPs that require ethernet. They ship with power injectors anyway. No need for a POE switch, but I love mine.
I messed around with all the consumer netgear, Asus, linksys, d-link crap and custom firmware, etc. Finally jumped into a 1u chassis running pfsense for firewall and unifi WAPs and gigabit ethernet POE switches for all my rooms / devices and haven’t had a single issue.
Of course, you get what you pay for… Doing home networking cheap means having to work out issues and that wastes time. My favorite device is my Wattbox IP based power switch. I can remotely switch on/off any outlet in the rack and reboot the modem, router, av equipment etc. Heck it can even do it smartly, it pings a website, if the ping fails it automatically power cycles the modem. Heals itself.