The basic rule I follow is that the case of the relativizer is determined by the role played within the relative clause by the entity it represents.
Give it to [OBJ whomever you admire __ most]. (You admire him most.)
Give it to [SUBJ whoever __ should have it]. (He should have it.)
Give it to [SUBJ whoever you think __ should have it]. (You think he should have it.)
But what about a 'raised' subject?
Give it to [?? ???ever you want __ to have it].
Does the raised form You want him to have it govern, or does the underlying role He HAVE it?
Does the language's growing indifference to persnickety punctilio direct me to whoever as the 'unmarked' or 'more natural' form?
Or is Great Mother English sending me the message that I'm pushing the boundaries of the language and ought to rewrite?