Hi TBill,
I should say up front that I run a company of about the same size - 10 on my core team, and about 15 independent contractors. So I wanted to offer the perspective of the folks you're working with, in case it's helpful to you.
I think you're right to cast this as a "moral" dilemma rather than a legal one. The contract doesn't require you to pay it back, and they can't demand it.
Instead it's a question of how you want to leave everyone feeling treated, and I'd suggest two things on this front:
1. Talk to them about it. The fact that you're their highest paid employee means they thought long and hard before hiring - about what kind of person they needed, whether they could afford it, how to recruit, and who to select. I'm not excusing the owner's management style at all. But I would be upset if my new hire up and quit so quickly without even telling anyone they were unhappy so that we could try to address it. The more specific you can be about what you want, and how you're feeling, the easier it is to sort out whether it can change. And at least they are on notice and feel you gave them a chance.
2. Err on the side of generosity. After this, the money is simply symbolic. The fact that you're asking the question here suggests that you're feeling at least a little uneasy about keeping the signing bonus and membership. Making the offer to pay it back may ease the sting of you leaving and forcing them to start over in their search. They may or may not take you up on it, but it will be appreciated, and also helps reinforce your frame that "I'm sorry, it just feels like we're not a good fit together."
However you handle it, assume that word travels. In every industry I know of everybody knows everybody, and everybody talks. At least a few of the people who work here are friends with the people who work at your new place because they used to work together at yet another place, or they're neighbors or they bowl together on the weekends. I know how young employees at companies in my industry in other STATES have behaved, because the owner and I went to school together or worked on a project in Switzerland eight years ago. There's no way the (former) employee would guess that I know that when they approach me at a conference interested in a job if I don't know anything about them and learn that they used to work for my friend you can bet I'll pick up the phone).
The $2k or $2350 investment in your reputation as a fair and generous guy will pay itself back in spades.
Good luck!