Without seeing the picture the only thing I can think of is my "go to" when I am stuck which is FMQ meandering. I used meandering and SID together on some quilts and they looked lovely. Also, if your circle too big to quilt SID at one go you can always do it in sections. When you start a new section, start it in such way that you overlap a few stitches from the previous section. Guide your needle slowly and you will be able to match the previous needle holes almost exactly. I know my explanation sucks, but I hope you got the gist of what I mean.