You sound like you're a bit unsure of yourself, or at least of your marketability in the job market. I'm pretty sure you'll be just fine. You need to take something that fits you, not take the first thing that comes along.

It sounds to me like you don't really want to be the Director - you want to be the doer. So look for that.

In terms of a resume, just say "I did these things". It won't matter that you did them for a startup.

(But what do I know? I've never been in the position of trying to persuade non-startup people that my startup experience was valid.)