my instructor always used to tell me to come off the clutch slowly, by degrees, the width of a pound coin each time (does that make sense?) either way, you NEED to come off your clutch nice and gently because as you know lifting up too quick causes a stall. You can apply more gas, sure, but you shouldnt lift the clutch quicker if you dont know the bite and the car well enough yet, because you could still stall and miss it anyway. Its just going to take practice. The car I learnt to drive in had a large engine, so I had to make sure the amount of clutch lifting and accelerator (sp?) pressing was balanced, yet my own car has a tiny engine, so only wants me to come off the clutch and apply a tiny amount of gas, so you just need to learn the car and work out what is most effective. The point is, make sure you have enough gas for the engine to be purring, but still come off your clutch gently.
Why doesnt your instructor let you hold it below the bite ? and do you get on well with your instructor ? Obviously I dont know and dont want to judge, but from what you've said, he/she seems a bit harsh? they should be constructive in their guidance towards you.
I would always suggest using the handbrake, as in the test it is expected of you, and the examiner wont think you've stopped properly unless its on. If you roll back in your test, you will get some minors for that, if not a fail.