You need to find out what the 3 letter abbreviation for STRATUS is and use that. More then likely you'll need to tell ATC what it is too when you call up. If you use 247357 in the plan/sartime, then tell them that's your call sign.
For example, Jabiru 24-1234 would plan JAB1234, when they call up as Jabiru 1234, ATC search JAB1234 and match you with the flight plan/sartime.
The limit of 7 characters isn't a function of NAIPS, it's because that's what the ATC system uses based on ICAO standard.
I agree with you that there needs to be a better system, such as the UL1234 standard, however most days it's not an issue for air services so until RA-AUS gets CTA access and it's a regular thing doubt it will be looked at.