Best glide is with a clean aircraft at best glide speed.
as I recall “longest time in the air glide” is a different speed, but doesn’t fly as far. I can’t remember the second speed as I’m of the view “why would I need that?”.
They are illustrated by best rate of climb and best angle of climb. I couldn’t get my head round them until I imagined best angle as a balloon rising vertically, but slowly.
I’d not go near flap until I was sure of the runway.
There’s no flap involved in best rate of climb.
I think what you describe is a practise dead stick landing on a runway.
A PFL goes down to 50’ over a field somewhere and ends with the phrase “we’d have made that” or “that would have hurt”. It might start as you rejoin the circuit, but I don’t think a PFL involves orbiting while you wait.
At something like ~300’ if it’s not going to work, you need to be telling your instructor what you’d do with no engine, in the early days “crashing” is a valid statement. “I’d try for that bit of grass” or “that taxiway” or some such, (before going around) is, “let’s just bin this and go around” isn’t
My first PFL, I picked a field covered in hay bales, when challenged I said “it doesn’t matter, we’re not actually going to land there”, that took a bit of explaining by my FI, and a change in my mindset.
back to the original question, check best glide in the POH, show your instructor, be thankful for what you learnt. It is training after all.