I have an idea that is too much for a comment. I don't have the code knowledge to confirm if it is allowable, or the time to do the research. I hope more knowledgeable members of this community will either improve or downvote this answer as appropriate.
Tentative answer begins:
Don't extend the 120v wiring up through your walls. Instead, poke the low voltage wiring up through your walls.
Based on description, all of your devices appear to be low voltage electronics with wall adapters. They are probably all running on 6-28V downstream of their wall adapters. So extend that low voltage wall adapter wiring instead. It has much less stringent safety and code requirements.
Begin Rebel Mode:
Get a spool of quality stranded lamp cord. Without knowing the power draw of your devices, I would suggest 14AWG--bigger than almost any electronic device cord. Snip the low voltage power cords of your devices and splice in a suitable length of lamp cord for your application. Make it long enough that you can plug in the network devices in the basement, have the three extended power cords run up through the walls, and connect to your devices in the main floor living area. The theory is that the wiring is low voltage, and is current limited by the wall wart power supplies, and code is relatively lenient on low voltages.
How to splice? To be blunt, if you must ask how to do the splicing, this is probably not be a good option for you.
End Rebel Mode
I realize that many members of this community are knowledgeable in residential low voltage wiring requirements and I hope those members will either expand this answer if possible or vote it down into oblivion if necessary.