I think scenario a is the appropriate one. You have a problem - are you going to stooge around all day and wait for the other engine to quit? I've never understood this on IR tests - an engine quits and you immediatley go into the hold for 15 minutes! You want the shortest and safest way down, and if you have to do a procedure, so be it, but there may be a more suitable place to go that has radar - you don't necessarily have to go for the nearest airfield.
In Canada, where they have a more practical approach, my examiner gradually socked out all the alternates until I had no alternative but to say I was going to bust minimums to get in - a better alternative to running out of fuel in the air. Perhaps your examiner was trying to bring a bit of the real world into your test.
Anyhow, if it helps anyone, here is what I teach about approaches:
An approach, especially a non-precision one, is characterised by large "steps", that is, major descents at certain stages, requiring large power changes that can be a pain with an engine out, so it's often a good idea to keep a consistent glide path as much as possible, remembering that the minimum heights at each step are just that - minimum heights. There's nothing to stop you being above them if you are actually descending under control. In other words, MDA (or any altitude, for that matter) is a height below which you must not descend, and not (necessarily) a height at which you must fly for the procedure, so you don't have to go to it immediately and make work for yourself in the final stages if you have a problem. In other words, it is a limit and not a target. My own preference is to descend down to around 100 feet above, and nudge my way down.
The idea on a non-precision approach is to fly level at MDA once you reach it after passing the FAF (assuming your heading is more or less in line with the runway) until the time you expect to be over the threshold (if you are not in line with the runway, you can expect a circling procedure, of which more later). Because timing is so important, it follows that your speed control should be precise.
Tip: Check the compass deviation - a couple of degrees means a couple of miles error!
You may obviously go down further if you can see where you're going (that is, you have established visual reference), but this should be at normal touchdown speed. It is a good idea to get down quickly enough to allow yourself at least a short time in level flight - ideally, at the visibility limits, especially as the MAP is often past the point from where a safe touchdown can be made. If you can't see anything by your estimated time of reaching the threshold, you must go around (more technically, if you don't have visual reference at the MAP, you must start the Missed Approach Procedure).
The reason why you don't do a dirty dart is that there are no performance figures for a go around in the landing configuration - you are taking quite a chance, and it is quite an urgent procedure - you have just tried to get as close to the ground as the height of a small apartment block, which is a pretty fine tolerance, given the velocities involved, and you don't want to be there if you can't see where you're going, so the routine is to add full power, then get the flaps and gear up. You won't gain much by pulling the gear up first at that speed, because it is producing minimal drag and will do until you are going much faster.
Drag varies as the square of the velocity, meaning that if you double the airspeed, you get four times as much. Conversely, reduce it by half and you get a quarter of the drag. Thus, at low speeds (as when landing), the drag caused by the gear has more or less the same effect within a small range or, at least, the incremental effect is less (review parasite vs induced drag). Put another way, the drag doesn't start to vary much till about 20 kts above your landing speed. For example, pulling the gear up at 60 kts may mean you won't climb at all. Doing it at 70 (+10 kts) could mean 50 feet per minute, 80 (+ 20 kts) could give you 100 feet per minute. So far so good, but 90 kts means 200 fpm, and so on.
The point is that, only from about 30 kts or so above your landing speed will you get any real benefit from raising your gear and expecting the decrease in drag to be the same as an increase in thrust.
Check it out with your own machine at a few thousand feet. Trim out in the landing configuration straight and level, apply full power and note the vertical speed (it should be a climb at this point). Then check the figures for every 10 kts above the original speed. You will find that, after about 30 kts, the rate of climb will reduce (after a modest increase), and your machine will even start to descend after about 60 kts! Airspeed isn't always the answer when you've got a lot to do in a hurry and you need to establish some priorities. Of course, you should not stay at such a low speed for long, as you need to get to normal climb speed, but at least you're getting further away from the ground. The point is, you can fly first and clean up later.
Phil