John, I'm also no lawyer. But (as my lawyer has pointed out to me) an unwitnessed verbal contract is worth at least 1000 times the paper that it's printed on. IOW -- nothing.
Your rights to something you've designed are smoky at best. You can copyright plans that you produce, but you can't copyright the thing made from those plans. You can trademark the name, and you can patent any innovations that you've made that are particular to the thing you've made. But unless you do those (expensive) things, there's nothing but courtesy to keep someone from going ahead and producing 'your' design with plans that they've drawn up.
It gets worse: none of this gets backed up by the courts unless you sue -- and that costs money. You can get a lawyer to write a 'cease and desist' letter, but if the recipient thumbs his nose at you then you're out of luck. Probably your best bet if you suspect (or know) that this is going to happen is to threaten to tell the world that they're producing the kit without your permission, help, or advice. Then at least they'll know that their efforts will be tainted in the public mind if they proceed.
There's information about this out on the web, if you want to dig for it. Start with "copyright" and "trademark", and go from there. If you really feel strongly about it, try to locate a lawyer who does copyright and trademark work, ask them how much they charge for an hour's worth of advise, then decide if you want to know badly enough to pay for it (figure that it's going to be a few hundred bucks).
And next time -- get a written contract. It doesn't have to be much, and it doesn't have to cover every contingency. If everyone's being reasonable it'll be short and friendly. Just set out your conditions, like "kit must be on the market by such-and-such a date or this contract is void", etc., and make it clear in all your conversations that no verbal agreements mean squat -- that it's got to be on paper, signed and dated before you'll put any weight on anything.
Alternately, just release your designs into the public domain, and don't bother.