FFF, I don't have an authoritative answer but present the following. An Alaskan Airways MD83 had a loss of control back in 2000 which resulted in loss of all lives on board. I mention this because a lot of work was done on investigating the accident with an
NTSB Report (pdf) which makes interesting reading.
(Just reread it and edited to add this)
The Safety Board notes that an airplane with flight control problems should be
handled in a slow and methodical manner and that any configuration that would aid a
landing should be maintained if possible.
............
The Safety Board concludes that flight
crews dealing with an in-flight control problem should maintain any configuration change
that would aid in accomplishing a safe approach and landing, unless that configuration
change adversely affects the airplane's controllability.
Recommendations include..
Issue a flight standards information bulletin directing air carriers to instruct
pilots that in the event of an inoperative or malfunctioning flight control
system, if the airplane is controllable they should complete only the
applicable checklist procedures and should not attempt any corrective
actions beyond those specified
...
Pilots should further be instructed that if checklist procedures are not
effective, they should land at the nearest suitable airport.
So you ask "Would it be a good idea, for example, to climb up to a safe height, and experiment at various different airspeeds, to see how the other controls react, especially as you slow down (after all, you will need to slow down to flare and land at some point)? "
From my reading of this recommendation, which may well be wrong, I would say you shouldn't. There aren't checklists for these things in spamcans, so don't be a test pilot and if it flies well enough to get it to altitude, it flies well enough to get it on the ground ASAP.