Where can I find published sources to support my claim about Hamlet? Is this claim sufficient? Could there be better?I have had the worst time...

You should read T. S. Eliot's "Hamlet and His Problems" (link: http://www.bartleby.com/200/sw9.html).

Not to spoil your efforts, but Eliot would disagree with your thesis and the premise of your research.  Eliot says that neither the play nor modern psychology can give insight into Hamlet, that critics inevitably project their own way of thinking into Halmet's: thus Hamlet become's Coleridge's Hamlet.

In other words, Eliot doesn't see Hamlet's problem as internal at all.  It's not idealism or cynicism or indecisiveness.  It's external.  He says that we must look at The Spanish Tragedy, the play upon which Hamlet is based, for our insight into Hamlet.  He says that not even Shakespeare fully understood Hamlet.

Eliot's thesis is:

...that Shakespeare's Hamlet, so far as it is Shakespeare's, is a play dealing with the effect of a mother's guilt upon her son, and that Shakespeare was unable to impose this motive successfully upon the "intractable" material of the old play.

Of the intractability there can be no doubt. So far from being Shakespeare's masterpiece, the play is most certainly an artistic failure. In several ways the play is puzzling, and disquieting as is none of the others.

Eliot has this to say about Hamlet's delay in killing Claudius:

...the action or delay is caused, as in the Spanish Tragedy, solely by the difficulty of assassinating a monarch surrounded by guards; and that the "madness" of Hamlet was feigned in order to escape suspicion, and successfully. In the final play of Shakespeare, on the other hand, there is a motive which is more important than that of revenge, and which explicitly "blunts" the latter; the delay in revenge is unexplained on grounds of necessity or expediency; and the effect of the "madness" is not to lull but to arouse the king's suspicion.

He says that Hamlet cannot express his problems in his soliloquies.  His problem deals with his mother's guilt upon him.  So says Eliot:

Hamlet (the man) is dominated by an emotion which is inexpressible, because it is in excess of the facts as they appear.

Gertrude is the key here.  Eliot says:

To have heightened the criminality of Gertrude would have been to provide the formula for a totally different emotion in Hamlet; it is just because her character is so negative and insignificant that she arouses in Hamlet the feeling which she is incapable of representing.

Eliot says we must look past the words, past the play, past ourselves.  Look to Hamlet's past, to his predecessor, the Hamlet of Thomas Kyd's The Spanish Tragedy.