peter005,
There is no aviation regulatory problem, you just have to negotiate a deal with your (whoever the training AOC holder is) proposed organisation.
What "having an aircraft on the AOC"means these days varies with the FOI/Team who/which is assigned to the org. If you can't sort it out with the org., and they blame CASA, talk to the FOI/Team Leader.
The real reason many flying schools don't like you using your own is they don't make as much money, although the excuses will vary, "insurance prohibits it" is a favorite one.
Having mentioned insurance, make certain you have that squared away in all respects, not just that training can be conducted in the aircraft. In particular, make certain all aspects of Workers Comp. for the instructor are covered.
Tootle pip!!