Green Goblin,
Aviate....
You probably learnt fast that even though you are in CTA (Class C), you are still in command and could of triggered twr of your position to prevent the go-around.....say at 2nm before the 3nm mark? Gives you 4.5 minutes to descend.
How many pilots in CTA just sit there waiting for approach to clear them for descent? All one has to do when it is busy is say " 2 minutes to TOPD"...This gives APP the heads up especially when it is busy going into BNE,SYd etc...It makes it more forgiving to everyone and reduces pilot work load.
In this particular instance it was not possible.
And of course you still work out a TOD point regardless of if you are in CTA and fly the particular profile you planned. Sometimes you can't help being held high until late and in the turbine side of things you can make those type of approaches easily. Piston aircraft are just simply not as flexible which ATC often forgets.