I'm sorry you're not closer or I'd do it for you:< One layer of stabilizer wasn't enough at all. Sometimes if the font isn't digitized properly you can get puckers, but to my eye this one is fine, the culprit is definitely lack of stabilizer.
I've had to pick out a lot of past embroidery work and usually cotton is forgiving. But, it would be a risk because we have no idea what kind of needle they used or if the fabric would be damaged.
Really, really I think you should try stippling around the first letter or so and see what you think.