Hi
I have an exact same dilemma. I think seed balls won't help much, though. Seeds will sprout for sure, that shouldn't be a problem. The question is whether the roots of your crops can penetrate into the soil and through the roots of the grass, before the it starts growing really fast.
I'd say the key is to seed some fast growing, hardy crops, like mustard (I've never sown anything you have on hand, but they should be just fine), as soon as possible, when grass is still 'sleepy', but just before the rain. Better risk another frost - mustard I've sown this year survived one without a problem. Mowing after you've scattered the seeds seems like an excellent idea.
I'm not familiar with Pacific NW at all, but I believe it rains a lot, doesn't it? This probably means that your grass dies back completely in the winter and starts growing rapidly in the spring. The positive thing is that your crops should be able to penetrate the soil much easier here, as opposed to places with less rainfall, where the grass' roots make for a much tougher competition. So, yeah, timing is really crucial. I don't know, but Fukuoka would probably agree
Anyway, good luck to both of us, right?