No experience with the clay product but since you haven't gotten an answer yet...
Can I ask how you went about handpicking? This is how I do it and it works pretty good.
First of all, no literal hand picking for me. I am too squimish for that - although cucumber beetles are really almost as cute as ladybugs, still...

When I hunt for beetles of any type, I carry with me a bowl of sudsy water - lots of bubbles on top - and a pointy tweezer. The ones for model making are real good for this as they are long or one for splinters which are thin and pointy at the tip or any tweezer really. I position the bowl underneath whatever they are eating and just knock them a bit with the point of the tweezer. Usually they drop off in defense into the suds where they will drown. Otherwise, if they crawl deeper into the flower, then I just pull them out between the petals with the tweezer. I've done earwigs, oriental beetles, japanese beetles, cucumber beetles and even a few colorado potato beetles this way. Works great and no poisons. The next day, I dump the bowl out. The beetles are dead and I go around checking again.

But maybe this is what you are doing now. How many beetles do you see walking around the garden? Are the plants just covered with them or are the centered around the blooms?