Undoubtedly, there are other WiFi Access Points and WiFi Routers which are superior to the single-core 1.5GHz CPU of the Technicolor (see its manual and specs in the question), such as the ASUS RT-AX3000 or Netgear's Nighthawk AX4 4-Stream AX3000, both of which offer multiple antennas to shape the signal better for a diverse environment such as yours. Remember, underneath it it, this is radio, and radio signals can be shaped and directed by their antennas.
If you get one, and call Cox tech support, they will provide instructions in how to turn off the WiFi and routing functions of the Technicolor device.
Whatever you buy, I'd suggest trying to buy one which complies with the WiFi 6 standard, AKA 802.11ax, to use the signal more effectively and get better speed when other WiFi 6 devices are on the channel exclusively. (If there's an older device on your WiFi, it drags the other devices down to its capabilities.)
Ideally, choose one with a removable antenna, like those above, in case you have one spot in your place which needs a highly directional external antenna to boost its signal. 2.4 GHz and 5 GHz antennas can be bought, or made easily and cheaply. You can also buy a signal shaper which drops onto an external antenna.
Until you do upgrade, perhaps a very old fashioned solution will work quicker and less expensively; shaping the WiFi signal with reflectors. Make a free standing frame to hold aluminum foil, or use an aluminum baking sheet, and put that reflector on the back side of the gateway, on the opposite site of the gateway from the devices which need better signal, a few inches away from it. Experiment with its placement. A curved parabolic reflector is ideal, but even just a flat or bent shape will work.
You can even make a passive repeater by connecting one antenna, next to the Cox box, to a directional antenna. The first antenna picks up signal, and the second antenna, coupled to it by a cable, focuses its signal where pointed. That's how the old cellular sick-on-the-car-window antennas worked; there was no direct connection, just signal coupling through the glass. There's a discussion of passive repeater details over at https://ham.stackexchange.com/questions/2146/wifi-passive-repeater-antenna-to-antenna-connection
You will not damage the Cox WiFi gateway by adding a reflector, unless you cover it with foil.