Sometimes it may be several things that cause ‘puckering’.
Are you using 100 % cotton fabric? Poly cotton puckers badly
Did you starch your piece before hooping? That helps
Have you hooped your piece taut enough?
Are you using the right stabilizer for the design or project?
Honestly, I don’t think it looks bad. I’d sure use it. I’d try a good pressing from the back covering the stitches with a pressing cloth or I have even used a clean xerox paper over the stitches.I wouldn’t use two different stabilizers, though.
cut-a-way is exactly what it says. To cut away around the design area. Look at bought sweatshirts or items that are embroidered and see how they trim or if it completely gone it’s tear-a-way or water soluble. You would not use water soluble on this project, tho.
Sometimes it won’t get any better than this, especially with words or writings. I do like your design very much. I haven’t seen it before but love the message.