It is one thing to have to cast an actor for a role. The difficulty increases when there are multiple roles to cast. Dramatic Interpretation insanity hits once the realization strikes that you have to cast yourself as several, special-as-snowflakes individuals. Should you be searching for a script that holds many characters that are just like you? Absolutely not. Not only does that mean the playwright is awful at characterization, it also is unrealistic. You will never find a piece where every character is perfect for you. So how is it done, this Dramatic Interpretation casting process? Easy.
Non-traditional casting. If you are a female and you wish to do a Dramatic Interpretation that has only one female role (and perhaps a supporting male one), you should not instantly be defeated by a gender barrier. You are competing in an event where you have to play multiple characters. Judges, audiences, EVERYONE will understand if you choose to do a piece where gender-bending takes place. It does happen. Just be certain that you are comfortable and able to play other genders. This also applies to other races as well. Performer discretion is advised though! There are times when roles are highly gender specific and a male playing a female lead (or in reverse) is inappropriate. Minor roles are where gender-bending should occur.
Main role. Your main casting concern should be to properly cast yourself as the lead. If you make a perfect Claudius, but a terrible Hamlet, your dream of performingHamlet as a Dramatic Interpretation should remain a dream (unless you do some clever cutting and focus your performance on Claudius). The rule is that your main character, the narrator, has to be a good selection for you to play. That is who the audience will see the most of, who should have more development and range, and the role where characterization portrayal needs to be impeccable.
"Minor" roles. There is some wiggle-room with minor characters. You still need to be able to perform as them, but if they are less developed than your lead you may be able to squeak by...for a time. Leaders in Dramatic Interpretation know that all characters matter and will tirelessly strive for all to be near flawless. It is distracting to pop from a fantastic Estragon to a mediocre Pozzo (Waiting for Godot, anyone?). Consider the possibility that you can select a piece with the understanding that the minor roles might be okay at first but can grow into developed, believable characters. Also, not all minor roles need to be used. Dramatic Interpretation allows you to decide if a character is a necessity. As long as they are not really needed (combining character lines is a fun way to "correct" a role you cannot perform) go ahead and ax them.
PRACTICE! All characters might not be you, but you can be most characters if you practice. This is acting! Of course there are limits and there are particular roles you would never be cast in if this were a play. But Dramatic Interpretation is not a play! There is the beauty. You can be the roles you long for which normally a director would never even let you read. Unless the character is so far removed from who you are that your portrayal is comical or horrible (or both) then practicing is the solution to performing a character you thought was interesting but one you would never get cast as.
Casting Dramatic Interpretation roles often leave novices concerned with how one can be multiple people. Do they have to match all their characters? Can a female play a male, or males play females? Am I suited for all these roles? The question shouldn't be can I, but why not? If the piece supports non-traditional casting, if you can tackle minor characters, and if you value PRACTICING ABOVE ALL ELSE, then that piece you were contemplating may still be approachable.