Thanks for the very detailed message.
I rather suspect your reasons are largely the same reason property managers are shifting to Direct Debit. Personally, I would never try to short the rent – I’m just not that sort of person. Until I setup an automated payment, I would often be angry with myself for mucking it up! 
On the other hand, if I were renting directly off the landlord instead of using an agent, I may be more amenable to use Direct Debit. The truth is that real estate agents are amongst the least trusted of businesses, and Direct Debit requires an inversion of trust compared to other payment methods. This is the primary reason I object to it.
My property manager has assured me several times that I can continue to pay with BPAY. More, I know his own boss knows my stance on this.
There have been no more problems with my payments.
Wade.