Just so we are clear, you, for the most part, can NOT transmit power, only signal. So on the receiving end you do need amps, whether they are in the signal receiver or in the speakers, you do need additional amps. It is unlikely that, at an affordable price, those additional amps will be equal to the quality of the amp in your current AV Amp.
If you are an electrician or electrically knowledgeable, then you know that as long as you have wood frame wall, and as long as you can get under those walls, you don't have to drill into the floors. You can drill up through the wall/floor seam and embed the speaker connection into the walls.
speaker terminal wall plate - Google Search
Being only marginally proficient in house electrical installations, I drilled a tiny hole in the floor right next to the wall in the area I wanted to install a low voltage connector. I pushed a tiny
'grain of wheat' light into the hold I drilled. In the basement/cellar, that
'grain of wheat' light allowed me to quickly find the edge of the wall. Then I drilled a larger hole into the base of the wall and ran my cable through.
I filled the tiny hole with a dab of wood putty, and when it dried, a drop of varnish. The hole was invisible once finished, and the cable has 'professionally' installed into a wall outlet.
Again, this only works if you have hollow wood frames walls.
Rapoo SE3 PC Wireless Speaker Receiver and Transmitter Adapter
Panasonic SE-FX65A Surround Digital Wireless Rear Speakers Sender Receiver Kit | eBay
[£24.64] - BX-501 Universal 2.4GHz Wireless Speaker Transmitter + Receiver Set - Grey + Black : Airyear Electronics Cheap Gadgets Shop
Alto Stealth Wireless 2-Channel Wireless Loudspeaker System | Sound | PA Speakers | ALTO | Lighthouse Audiovisual
I'm not recommending any of the above, simply pointing out that such devices do exist, though they are becoming more rare everyday.
Steve/bluewizard