First of all, let me say thank you! to those of you with your helpful comments. I can see I'm not alone here!
It just so happened that as we were out & about yesterday, we were near the Home Depot. So of course I stopped in. Plumbing aisle. Got this:
Then I came home and cut little pieces, and cut those pieces open - like this:
Anyway, here are the rest, all nicely tucked into their...tubes, I guess?
But I wasn't done...that thing they are in - it looks nice now, but it still gets in the way. I need it off my table. I have so precious little space. So here's where the bobbins are living now:
cabinet. Right under the thread (duh, like you couldn't see that).
("Rachel! You're a genius!" you say? No. I got the idea from Pinterest. See my post from yesterday. ;)