Since you say that you have little experience above 12,000', I wonder why you are singling out HAPE and excluding the other two conditions that comprise the spectrum of high altitude illness: AMS and HACE. AMS is certainly far more common than HAPE.
Regarding dexamethasone and other drugs in this context, here is what I wrote on the
WPSMB some years back:
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A recent question (Aspirin or Ibuprofen or ?) is very pertinent for the unacclimatized Mt. Whitney visitor. It's addressed in a paper in the New England Journal of Medicine (Peter Hackett, MD, and Robert Roach, PhD. "High Altitude Illness", Vol. 345, No. 2 - July 12, 2001). Hackett is probably the best high-altitude pathologist in the world, and Roach is a well-known researcher. This is a survey paper with fully 76 references. If you don't want to wade through what follows, the findings are that aspirin has proven useful in prevention of high altitude headaches, and ibuprofen in treatment.
Headaches are one element of the broader topic of acute mountain sickness (AMS). For the broader question, one paragraph in the paper is long but especially pertinent: "For the prevention of high-altitude illness, the best strategy is a gradual ascent to promote acclimatization. The suggested guidelines are that once above an altitude of 2500 m, the altitude at which one sleeps should not be increased by more than 600 m in 24 hours and that an extra day should be added for acclimatization for every increase of 600 to 1200 m in this altitude. For example, as compared with ascent to an altitude of 3500 m in a one-hour period, a gradual ascent over a period of four days reduced the incidence and severity of AMS by 41 percent. Most experts recommend prophylaxis for those who plan an ascent from sea level to over 3000 m (sleeping altitude) in one day and for those with a history of AMS. Acetazolamide is the preferred drug, and dexamethasone is an alternative; both are unequivocally effective; the dosages vary. The combination was more effective than either alone. Although controversial, small doses of acetazolamide (125 mg twice a day in adults) appear empirically to be as effective as larger doses, with fewer side effects; the minimal effective dose remains uncertain. In two controlled trials, Ginkgo biloba prevented AMS during a gradual ascent to 5000 m and reduced both the symptoms and the incidence of AMS by 50 percent during an abrupt ascent to 4100 m. With respect to headache, prophylactic aspirin (325 mg every four hours for a total of three doses) reduced the incidence from 50 percent to 7 percent. Reports suggest various Chinese herbal preparations might prevent high-altitude illness, but controlled studies are lacking. The notion that overhydration prevents AMS has no scientific basis."
Another paragraph, in part: "A small, placebo-controlled study showed that the administration of acetazolamide reduced the severity of symptoms by 74 percent within 24 hours. Multiple studies have demonstrated that dexamethasone is as effective as or superior to acetazolamide and works within 12 hours. Whether the combination of acetazolamide and dexamethasone, because of their different mechanisms of action, is superior to the use of either agent alone is unknown. In two studies, a single dose of 400 mg or 600 mg of ibuprofen ameliorated or resolved high-altitude headaches."
I'll add a personal opinion. While overhydration may not prevent AMS, I agree with the others: Staying sufficiently hydrated is one of the most important things you can do. It's difficult when you're not feeling well, but drinking at least a half-liter an hour while you're hiking is a good goal - a liter an hour if you're sweating a lot.
(Note 1: The original paper can be viewed
here.)
(Note 2: More recent studies have discounted the effectiveness of Gingko biloba treating AMS.)
(Note 3: A good friend of mine, who has been climbing in the Sierra almost as long as I have, suffered badly from AMS on every trip. About 15 years ago, a local physician (also a mountaineer) prescribed a small dose of dexamethasone for him. Now he takes it every time, and does not have any symptoms.)
