Nygal, Mb is right. Everyone develops their own way of doing pp. I leave the paper on when sewing the sections together. I place the sections together, use a long pin straight down thru any star points to match the star points then use the small red binding clips all along the section. I can remove the pin and sew the seams removing the clips as I reach them. I don't have any trouble with my machine sewing thru all the layers (except if I've had to use scotch tape for some reason--machine skips on tape).
As an aside, I know someone will "yell" at me for spending the money on the red binding clips and not going to the dollar store and getting stationery clips. For me, the red clips are worth it: they have a flat side so the seam rides flat thru the machine and slide right off as you get to them without having the section pull out of the machine. I do a lot of paper piecing so the extra cost was worth it. If any one is interested, I got 50 of them on Amazon for under $20.00. (Sorry if I sound defensive but on another thread there was a lot of arguing about the cost and benefits LOL).