my excuse is that we were fannying around overhead for ages doing 360's waiting for clearance to start.
If you're practicing for a possible real event, practice like it's real. If your engine quits, you're not doing 360's waiting to start, you're headed down, you've picked your spot, you've started. Every other pilot will get out of your way, every controller will let you do it in your time - I know, I've forced landed into a busy airport I was only overflying, 'right place' right time, no problem. Of course, during a practice maneuver, you're not going to cut off traffic, and upset airport flow, so the whole exercise was poorly introduced by your instructor. I don't set up a practice for a student, in practice circumstances which are designed to train real decision making and technique. It teaches the wrong priorities. If it quits, get it on the surface safely, damage free if possible, everyone else will give you space if they know you're having an emergency ('makes a radio broadcast a good idea, if you can).
Don't extend any flaps until you know that you have the landing site made. If in doubt, don't extend any flap until you have the landing site made. Once you are going to land (hopefully, on the site you chose) extend all the flap, even if they're in transit as you touch, keep 'em coming, they slow you down.
As you glide, if you suspect you're a little high for your chosen spot (which I hope you are, 'till close final) use a sideslip to get rid of excess altitude. Every training airplane will sideslip very effectively (except an Ercoupe, you're not training in one of those). A sideslip allows you to modulate the approach rate without changing speed - slip, unslip. Once flaps are out, you can't effectively retract them if you judged wrong. You can, and should unslip as you near the surface. But (and I have done it) if you need to, you can touch down a 172 in a slip, while extending flaps. I'll get drawn into a discussion about slips with flaps in a 172, fine. In the mean time, the plane will do it fine.
Best (optimum) glide speed is published as a certification requirement to tell you how far you can glide, not how easy it will be to make a well judged approach from that speed. Many instructors really don;t know this, and thus don't teach it. Yes, you can, and must demonstrate a PFL at best glide speed for the plane, but that does not make it the best way to PFL, it's just what the book says. If the engine quits, look below you for a spot, not halfway to the horizon, and then spend a thousand feet of altitude wondering if you're going to make it.
Have a read of the text from John Farley's book which I posted recently. What John writes works, and I train it to my students. I can't tell you to not learn what your instructor is training you, it's in the POH, and another pilot like your instructor will examine you, and expect you to do it that way, but it's not the only way.
At the end of your actual forced landing, I would rather read that you went through the far hedge at 20 MPH 'cause you could not get it stopped, than you couldn't post, because you undershot an hit a car on the road short of your spot. For a forced landing, mis judge too fast/high, not too slow/low. If you have to have an accident, have it slowly. If you have to explain to your instructor/examiner you mis judged, may it a not so serious misjudgement!
When your engine quits, and you're committed to an actual forced landing (four times for me) you'll be really focused, and you won't be caring about what anyone thinks of what you're doing - you'll explain later!
between us we then mucked about with the flaps
Ah... no. Either you're flying, or your instructor is. If you are the pilot, another person in the cockpit (even senior to you) should ask you for concurrence, before moving things. If they (being more experienced) feel compelled to move things, they should ask to take over. Indeed (and I've done it) after taking over and fixing things, they may give it back to you to continue. If your instructor has left things go to the point where they suddenly need to fix something, without some advice to you, they missed the mark. If the instructor is beginning to think: "Gee, DB may need a little flap to make this work..." Instructor should say to you: "DB, I think this is going to take a little flap, I suggest you extend 10". If you're task saturated, you may ask for them to do that. Ultimately, extending some flap in a 172 should not task saturate you, and a helpful hint should still leave only you flying the plane.
This is a lesson in pilot briefing, both before the flight, and during. A 172 is a single pilot plane, it does not require two pilots to fly it - so two pilots shouldn't! (unless the briefing to do so is really good!).