Thanks all, for the encouragement and suggestions. It is true that when I got it more than a foot from my face, it started to look a little better.
NativeTexan, (and other helpful posters!) I think I was erring on the side of not putting the needle into the background and it made the fabric edge poke up instead and look gross along the outside of the curve..
But I am worried that I shouldn't have the red stitches showing over the edge of the fabric and onto the green background. Are there applique police?
Of course if I do a buttonhole stitch it will cover up the whole edge so it won't show, right? Can't wait to go home and try it out!!!
For the glue-up - I traced the template shapes onto fusible web paper, cut them oversized, pressed them to the fabric, cut them out on the template lines, peeled the paper off, pressed the fabric pieces together against a piece of translucent baking paper, under which was the black-and-white drawing of the whole project, peeled it up, and ironed the completed flower-thing and the other loose pieces to the background. It stuck well, rather stiff, and I did not use a tear-away behind the background.
I've also found out that I should change the stitch length and width to accommodate the pointy bits and the tight curves. And whoever said be sure to put down needle and move fabric when needle is outside the fabric - hohoho easier said than done. Going as slow as machine will go, using foot pedal, still miss it. Had to do one up-needle down-needle button at a time.
Well, hurry 5PM!