I don't think the solution goes through presenting yourself like someone other than you are. The solution goes through presenting yourself just as you are, and showing this isn't an impediment to hiring.
If you want to give them reasons why they should hire you in spite of this, apologizing probably isn't going to be ideal. An apology means you think your own behavior ought to get you eliminated, but you'd like to ask them not to do that and to overcome that sentiment. That is not going to work. For one - and as with all negations - you can't pretend to give someone the idea of something and at the same time expect they'll forget it or not think of it. That's not how the brain works. And second, you can't be apologizing for everything you do, or, if this is truly your character, you'll have to be apologizing quite often, and that's not sustainable, so better not start at all.
I'd do one or both of these things:
First, talk about diversity in the workplace, and even mention the issue of mental health. Talk about how you enjoy working with very different people and how you learn from them and enrich everyone's experience. These are values, and they're often shared, or at least should be. In some countries they're even rights (of non-discrimination). Also by talking about the issue of mental health (find an appropriate time to introduce this), you show them you've got no fear, also as you imply it might apply to you, you show them you know yourself and you can be your own critic; so you're not out of control (or if you're at times you can still regain control). Grab some statistics, talk about how nobody's perfect, talk about opinions, perceptions, self-awareness, and that'll go some way to earning you the 'right' during the interview to be your own judge and not just be judged.
The second is more practical. You have to find a way to free yourself up, even to the unexpected in you, and show that you can be receptive to your own behavior -and that of others- in an humorous way. And the trick is this: it's hard to find humor about something you do you wish you hadn't done (so probably just skip over these), but easier to be humorous about something you know you're doing consciously, especially if you think it's got a chance to be funny, an ice-breaker, or got a chance of being well received. So try to think of jokes or incidental remarks dashed with a bit of irony or comedy, which, practically, could be thought of as a reflection of your own condition (of those other moments you do that involuntarily) that, you show, you can incorporate the essence of, back into your life and in your own behavior / your discourse, in an accepting, humorous way. Be lightheartedly self-referential, be almost like a mime of yourself. If you're aware of something that makes you stand out, refer to it, exaggerate it just a little, and find a positive way of bringing that to their attention (or something similar), and bring that into the room. This will show you're not afraid of it, and prove that incorporating this aspect of you into reality poses no danger. So, show self-awareness and, through accepting yourself even to the point of being willing to present this as part of your identity, let the others feel that they can do likewise. Make them think that, regardless of the outcome of the interview, you're out to having a good time, and you'd like them to have it also. Smile (no one's frank smile is ever turned down).
Think about these. Ask advice from people who know you well. Don't overdo it (otherwise the interview could run well off-topic), but don't leave it out either. Experiment (think of several strategies so you can give yourself the choice). Play with it in varying doses. Don't force it (and when it doesn't appear to work, don't panic). Enjoy your interviews.