I know custom firmwares skip the signing process but I don't know if a request has to be sent and a response has to be received in order to restore anyway.
Hmm, just re-read your initial post. It says you have the new bootrom. You can't use CFWs at all then. The Firmware Umbrella, where local SHSHs are used, won't work either because the request/response actually goes through the internet even though both the files and the server exists on your own computer.