In fact, I have had time to think further about flaps since I first posted.
Based on a C152, which is the type I know most intimately, but my argument would probably work on most (but almost certainly not all) other types:
In a fully serviceable aircraft, when flaps are lowered, if no trim or power change is made, the aircraft will tend to pitch up, with a large reduction in speed. If the aircraft is then pitched back to its original attitude (and trimmed), a lower speed will be observed than before the flaps were lowered. In order to re-gain the original speed, it's necessary to pitch down even further. It is the last pitch down which gives the better forward visibility (and larger flare) which we are used to seeing on a "normal" approach with flaps. However, the initial tendency of the aircraft when flaps are lowered is to pitch up, so therefore a small amount of flap may be beneficial in preventing the nose-wheel from touching the ground first.
Again, in a fully serviceable C152, imagine you set a cruise power of 2200rpm and trim. Now, reduce power to around 1500rpm, lower 20 degrees of flap, and do not touch the trim. The aircraft will tend to settle in an attitude slightly lower than cruise, with a steady rate of descent, and a speed of around 70kt - pretty much an ideal configuration for the initial stages of an approach. Why the pitch down in this scenario, but the pitch up when using flap alone? Because of the power reduction. And this power reduction is, in fact, necessary because otherwise the aircraft won't descend. So this tends to contradict my previous paragraph, because the previous paragraph would only apply if no power changes were made.
When my though process got to this point, I figured that the best thing to do was go and try it and see what happens, adjusting power and flap whilst keeping my hands off the controls and noting the results. But of course trying this in a serviceable aircraft is not a valid test, because in a serviceable aircraft there is nothing to stop the change of flap settings and speed resulting in a small deflection of the elevators when the aircraft is flown hands-off.
So, final conclusions - if this happens, climb up to a safe height, and experiment with various flap, trim and power settings until you find one which gives you a nose-up attitude with a low speed and a rate of descent. This is not something which can be done in advance of the failure; nor, I think, can it be done theoretically by sitting around talking about it, because there are so many factors that work both ways and it is not possible to tell which factors are going to override the others in practice.
Now my brain hurts, and I'm going to go and lie down somewhere.....
FFF
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