Thanks everyone for the help. Am replying to say thanks and also in case someone else has this issue in future.
I have tried various suggestions, and this is what I finally came up with. Hope it makes sense.
Using thin see-through paper, I traced the shape from the pattern and added seam allowances - one each for the mirror sides of the wing. Marked the shape so there was no confusion about the way which piece faced etc.
When I do foundation piecing, after I have added a piece I fold back the paper at the next seam line and trim the just-placed fabric to the seamline plus 1/4" seam allowance. This gives a straight edge to line the next piece up with.
I folded the segment pattern at the seam line - putting the allowance behind the shape, and then placed on the fabric to isolate the design I wanted to use.
Sketched a couple of features of the fabric, and then placed the two pattern pieces back to back to check the sketches matched up.
Cut the fabric for each side to the seam allowance on the first side to be sewn, and allowed about 1/2" on the other sides.
Placed the traced shape face up in the location on the foundation piecing, matching the first seam line. Because the seam allowance part was folded behind the pattern, the cutting line was correctly placed within the shape. The dog ears of the triangle came out each side behind the pattern piece.
I then placed the fabric face down (RST) with the cutting line matching the cutting line and dog ears.
Sewed on the seam line.
Pressed the fabric in place and thank goodness it was perfect! On both sides!! Big woop here.
I have yet to try with other shapes but it may well work with them. The critical thing is getting that first seam right, and using the transparent paper and viewing the cutting line is what made the difference. So pleased to have sorted something a bit logical rather that cut, sew, pray!
Easy when you know how...