La idea con los retransmisores de señal me parece la mejor, pero vas a tener que poner mas de 3 me parece.
Si lo intentas con cable, recuerda que con cables de red Cat5e el máximo es de 100 metros tb, asi que también tendrías que poner switches en el medio.
Otra idea seria intentar 802.11n
Según el texto de abajo alcanzan hasta 300 pies .. ( 90 metros)
Get complete home wireless coverage like never before.
Wi-Fi networks are all about convenience. 802.11n provides high-speed coverage at ranges never before possible—providing wireless access anywhere you go.
* While existing networks begin to fade at distances as short as 100 feet, 802.11n maintains high-speed connections at greater than 300 feet—giving you three times the range.
* 802.11n was built to solve range issues with techniques that minimize interference, optimize data channels and increase the sensitivity of Wi-Fi devices.
* And while other WLAN standards perform at or below 1 Mbps at 300 feet, 802.11n can perform as high as 70 Mbps at 300 feet—a staggering difference.
Bueno, espero nos cuentes que has hecho
Saludos!