Surely this is all about doing what you’re used to. If you generally do a constant aspect approach to land when the engine is working then do one when the engine stops. Seeing as I fly out of an airfield where the standard circuit is a rectangular circuit, I fly (and teach) a base leg and final approach into a field. The point being is that I know what it should look like because I’ve done that type of approach many times before.
IMHO an engine failure should be treated as follows:
1) Immediately select carb heat (if appropriate)
2) Establish best glide speed
3) Make a plan, i.e. select field taking into account size, shape, slope, surface, wind direction undershoot and overshoot, inhabitation etc, and then select a 1000 foot point (a point where you should be at 1000 ft on a base leg into the field)
4) Do the WHY checks. Fuel on (change tanks if appropriate), (carb heat check on), fuel pump on, mags on both, mixture rich, exercise throttle, try starter.
5) If the engine doesn’t start, call Mayday.
6) Fly to the 1000 ft point (doesn’t matter how, as long as you get there)
7) Now comes the judgement. Aim to land half way down the field, too high, fly through the extended centreline, too low, cut the corner. Use flaps as necessary to move the aiming point back towards the field boundary.
8) Perform the shutdown checks, remembering that if the flaps are electric then don’t switch the master off until sure that no more flap extension is required.
9) Brief yourself (and pax) to tighten straps, brace etc. Unlatch door/hatch
10) Use short field landing technique, a higher than normal vertical speed on landing will help remove the kinetic energy. Keep weight off nose for as long as possible.
11) Evacuate as quickly as possible, taking the first aid kit and fire extinguisher with you.
12) Telephone police and/or ATC with the news.
As I value my licence, I tend to perform a GA just above 500’agl, however by then I know whether we’d have made it or not.
I’m not saying everyone should do it like this, it’s horses for courses. As long as your technique gets you down alive, then it’s been successful.