I’m not sure about a GSM booster, but a smartphone can be made to emit Wi-Fi, whose range can be extended with a Wi-Fi Extender. Place the phone into an area with good coverage (by a window perhaps?), activate the WiFi hotspot, and connect your other devices to the phone’s WiFi network. If the range is insufficient try switching to a lower band (2.4GHz signal will travel further than 5GHz) and if that’s still not enough buy a WiFi Extender, set it up to connect to your phone’s WiFi network and connect your devices to the Extender’s network.
I’m not sure how doable this is, but there are routers or tablets that can accept a SIM card. You could maybe ask your service provider to give you a second SIM card tied to your number that you could put into it. I’m not sure how calling or texting would work with two SIM cards tied to the same number, maybe your provider could disable these options on the new SIM? I don’t know anything about the inner workings of telecommunications, this is just an idea.