You don't turn in from the same downwind position as a powered approach.
I am confused. When I learned to fly I was taught a glide approach was done by turning base in the normal way (maintaining altitude) then when you think you can glide in from level base, just close the throttle and assume the gliding attitude.
It is not a practice forced landing from downwind where ATC needs to know for separation spacing. No need to tell ATC since it is a normal circuit turn on to base. If due to traffic ahead you are unable to turn base in the normal position, then extend downwind as needed while maintaining level flight until on final. Then when you reckon you can make it from there, close the throttle and commence the glide. The aim of the exercise is to practice gliding to land as against a powered approach to land. It is not a forced landing practice which is normally conducted in the training area.
when training flights required time to load up on the brakes for a short field take off
Holding on the brakes for a short field take off is unnecessary. It causes unnecessary propeller stress due bending moment and the extra take off ground run distance from a closed throttle take off (assuming less than five seconds from idle RPM to full throttle) to a full power take off on the brakes, is practically un-measurable.