i have a profile threaded to threadless adapter
and it has a clamp area just big enough for the stem
but the quill has a couple inches of height adjustment

and
the stem in no way need to be against the headset
as the headset is the threaded type
the adapter basically turns a clamp on stem into a quill stem

and
if two inches of quill extension
plus a high rise stem
doesnt get your bars high enough
then i suspect you have the wrong size of bike
or a bike that is otherwise ill fitting
to the point of being impractical for you to ride