I generally use the term PFL to describe a practice approach somewhere away from the airfield. For the final part of the forced landing, practiced in the circuit with idle power to touchdown, I tend to call it a glide-in landing. Obviously you can combine the two into a PFL culminating in a full stop on the runway, but the downside of this is that you don't have much room to change your mind during the exercise and will have to land on that runway, which makes it suitable for advanced PFL students only (my terminology).
TheOddOne already mentioned that you only use flaps on final approach to bring your touchdown point back to the start of the field. The best way to judge whether to use flaps is to look at your planned touchdown point while gliding at chosen speed towards it. If it is moving down on your windshield, you are going to overshoot it. Add one stage of flaps, acquire new attitude to maintain chosen speed and reasses. If it is still moving down, or too far down the field for your purposes, add another stage of flaps and adjust your attitude again. Repeat until happy, down on the ground, or you run out of stages of flaps.
Your original suggestion (add flap and raise the nose) is one I would advise against. In a C172, especially adding flaps beyond 10 degrees will have you put the nose down significantly just to maintain glide speed. Keep in mind that you need a few knots to be able to perform any kind of flare at the end. If you add flaps, the increased drag will cause a speed decrease and you will be eating into this margin of speed. Raising the nose more at this point will only do more damage to this speed margin, and it is not something that you can get back in any way. In my view, 'stretching a glide' is an impossibility.