I've never heard of a beer machine, but if you have too much headspace I can't see you having much luck carbonating your beer. I'll have to google this contraption to get a better idea of what it is you're using, but if CO2 cartridges are an option, then that may be your best bet.
EDIT: It sounds like you have the option to add CO2:
The Beer Machine has a pressure release valve to keep the naturally produced CO-2 inside The Beer Machine constant, a carbonation unit to add CO-2, and a dispensing system so no bottling is necessary.
I'd try that route first.