Oh the frog stitch is my least favorite. (Rip-it! Rip-it!)
But we all need to do that now and then. Patience is a virtue. And your piecing and fabrics are very nice on that piece, so it would be a crying shame to just ditch it.
You've gotten some really useful tips here. The medium value thread color will be less noticeable--maybe a nice medium grey? The pinning is crucial. But the practice is key. Practice practice practice.
I doodle a lot, even now, and I have been machine quilting for almost 10 years. I doodle on paper, and on dry erase whiteboards and I doodle on fabric with my machine. Just plain old muslin works fine , but it's so boring. So lately I have been using up some stash that I wonder why I bought, and practicing new designs on that. Practice practice practice.
The regualr designs are more difficult, and the random designs are simpler. Here is an interesting blogger who is machine quilting on her domestic machine and trying to come up with a different design every day. She has some beauties that are a nice change from stippling and no harder. Practice practice practice.
Please let us see it after you have reworked it. I'm sure it will be worth your time and trouble. Good luck!