If Shakespeare wanted to make himself known to the characters in one of his plays, the only way he could do it would be to become one of those characters.
Jesus is the way, the truth and the life.
Good grief! There is misguided and then there is just plain daft, and this is the latter.
The one aspect you do highlight, probably unknowingly, is one I thought you'd try hard to avoid: which is that there is less evidence for Jesus than there is for some of the historical characters as portrayed by Shakespeare putting fictional words in their mouths: which, of course, may well also be the case as regards what Jesus is claimed to have said in the NT.
What Richard III 'says' in Shakespeare's play is acknowledged fiction, and what Jesus 'says' in the NT is indistinguishable from fiction - well done you!