My dad, now actively involved in the project, felt very strongly that I should use staples; but I was worried that they'd show. After much contemplation, delay and general procrastination, I finally invested in a $3 glue gun tonight. The clouds opened up, the sun finally started to shine and the angels did sing.
The Ottoman has trim!
That's Beatrix in the photo with Tallulah, not José. José and Tallulah seem to have had a falling out of late (I think because he keeps trying to steal her limelight) so Beatrix has stepped in as the new BFF.
A local craft store was giving away round "table tops" (pieces of wood) that are about 3' in diameter. I snapped up a couple of them. As soon a I can find the right fabric, I'm going to make a matching round ottoman to go with this one and replace the old coffee table entirely.