I have no trouble getting the data from the module as required but without re-inventing the wheel and writing the parsing code myself I can't figure out how to use for example Tiny GPS to simplify the task.
You can't. TinyGPS doesn't know about GPSACP mode.
Is there a way to get this Library to recognise the GPSACP: sentence
Yes. You can add code to TinyGPS to make it parse GPSACP sentences, IF you know what all the values mean.