As you can see from the examples below, one's eye goes right to that line. It is continuous seam and it dominates the block. This is not the effect I wanted. I wanted to have a rose that kept its shape.
Thanks to the various connections of blogland and ultimately Tonya, I was put in touch with Brenda, who kindly wrote a tutorial on making the rounded roses that she has used in several of her quilts. I tried the technique and like it, and I will make more. I need to refine the backgrounds, as I do prefer the log cabin backgrounds to a single color background. Yes, you can do curved piecing with log cabin backgrounds. However, with the log cabin background, the long seam problem is still lurking, especially if one chooses a darker fabric.
While trying to puzzle out a solution, I looked through some of Ruth McDowell's books and enjoyed the incredibly wonderful combinations of fabric she uses in everything she does. It dawned on me that "made fabric" looks a little bit like Ruth's multifaceted pieces. What if? What if I used made fabric with my roses? I dug out some already made fabric and began fitting it around some roses. The result was just what I wanted. The rose remained a rose and all the little seams of made fabric help to disguise that pesky long seam. Ahhh.
(The phenomenon of the continuous line and the effect of off set seams is discussed in Ruth McDowell's book, Design Workshop. I discovered that after I had sewn the made fabric to the roses. It was nice to have thoughts confirmed and further explained.)