My approach on interviews is to try and remove as many reasons possible for the person to not give me the job.
These include, dressing the best I can, ( In this instance that means a suit) Nobody won't offer a position because you were wearing a suit, but they might because you weren't.
Try to avoid bringing up anything negative comments about myself.
A small thing but I always avoid aftershave, I might think it's the best smell on earth, but they might literally puke at its slightest hint.
Given that you are asking them to consider you and pay more than the advert, you need to show them that you are better than everyone else, and small things like dress can be the difference.
Most people don't like rejecting people, so will jump at anything that they can to justify an easy decision for them, so don't give them an easy reason.
Tbh, given that your asking, I think you already know that you should, but you'd rather note, so were looking for some amount of confirmation of your thinking