Embroidering on these koozies isn't the problem, though this illustrates what I learned about getting too close to the edge 
the problem is that my sewing machine skips about half the stitches while sewing up the side seams. Instructions only said to zig-zag the side seams. They're for fundraising so I'd like to make them look professional.
The machine has plenty of power - it's an older model Brother that's a real workhorse, and I had the same problem with my old Singer 401, another workhorse. It is something in the thread, tension, needle, I think - just need to find the secret to sewing this stuff.