While I was doing the survey to my font, I took notes about many unusual characters –unhappily, not to all them. My sources are many sites about linguistics, Wikipedia, proposals presented to Unicode Consortium and also articles about minorities and their cultures.
Yes, I'd put dieresis above ḧ ascender. It would become very tight at the top of n-like curve.
Especially in heavier or more condensed fonts.
One addition to an ancient discussion: If your ascenders are taller than the cap-height, ascending letters with accents may benefit from being lowered to align with the caps.
I agree that Adobe's choice of putting the accent over the ascender is unfortunate.
But in common with accents over ordinary lower-case letters without ascenders, at least there is not a large amount of empty space under the accent.
Which leads me to ask why no one has mentioned a third possibility for h-circumflex in this thread; is it so obviously bad that it is clearly to be excluded from consideration - or is it in violation of a basic principle that accents must be outside the letter shape?
That is, the accent is clearly not outside the letter shape - but is there a rule that it must be?
It is not my intention to propose this as a model but since there appears to be no specification of what Esperanto is expecting, we may simply make a little experience with the type of equipment that was available when the alphabet came out, namely typewriters. When I started typing, typewriters were mechanical and we would first type the accent, the carriage would not move, and then we would type the letter. That way we could get an eacute by first typing the acute and then the letter e.
There is still an "old" Selectric typewriter in a locked room in my department (and it is still used once in a while, I am told). I just made the experiment, typing a circumflex and then the letter h. Here is the result
Without a spec, I presume that this is roughly what the first esperantists were expecting to get as an h with a circumflex.
Added: it seems that this was also acceptable in printing since the 1905 edition of Fundamento de esperanto contains the following specimens (page 27)
where the last occurrence is the name of the letter as printed in the text.
Looking at the other thread, I see you beat me to the suggestion I made! And, of course, we were both beaten in 1905 - although the other forms were also used then.