Do you by any chance know why the limitation is 128 bytes and if i may simply open the library files and change the value?
To know the why I would have to ask the developer. I guess it's because 128 byte is more than enough for the majority of use cases and because the library was developed for an Arduino (UNO has 2k of RAM) and not an ESP8266 (64k of RAM). In the embedded world usually you don't waste RAM for stuff better done on bigger machines. You seem to prepare the JSON for a web application on the ESP and transmit that using an MQTT server. You probably should re-think if that concept uses the right tools for that task.
But to answer you question: it seems that you can simply increase the value in the .h file.