You didn’t say if you followed CountryPaul’s advise and checked for other channels?
Wireless is a whole different ball-game to wires. Again, it has no relation to your internet connection speed.
It is also a half-duplex system. That is, it can’t send and receive simultaneously, so when they say 866 Mb/s it usually means 433 send and 433 receive etc.
It is also sharing the airwaves with other devices on the same channel. If people are being sensible and sticking to channels 1, 6 and 11 there is a mechanism for two wireless point on the same channel to cooperate and share the channel. Of course, this may mean you have to wait while your neighbour sends something, slowing real time transfer down a little etc. 1, 6 and 11 are far enough apart to be separate. The channels in between overlap. If your neighbour thinks he’s being clever by using, say, channel 8, it just causes interference without them being able to talk to each other and cooperate and slows things down even more. (5 GHz is better in this respect as the channels are far enough apart not to overlap).
Wireless also has a whole lot of other baggage going on, such as the change in signal format between ethernet and 802.11 then back again. Encryption/decryption etc.
Your best bet is to proceed with the plan to put wires in then put a wireless point in each room using wireless roaming. That is, same SSID but channels 1, 6 and 11 arranged so no two adjacent stations use the same channel.
