Came back too late to edit, my little Brother does pretty good with what I call "sewing into space" but some machines balk a bit at that. You can overlap those points a bit as you feed them through since you are going to cut them off anyway. That is, actually ride up the next piece on the end of the previous piece.
Or (and this is one of those times when a picture is worth a 1000 words but I don't have one yet) you can jog the fabric over a bit and sew the alternate seams, that is, the right seam, jog the next block over and up at the point and then the left seam. You can also do this when piecing a lot of little triangles, the type that love to get sucked down, flip every other one over so the points form a straight path for the sewing machine.
I've become a big believer in my 1/4" quilter foot -- I simply couldn't piece with a zigzag needle plate and foot. I do want to mention that I've been very pleasantly surprised with the accuracy of the one I'm using on the "cheapo Brother". Also that the needle threading assist is very helpful to me with my vision issues. I am not a machine snob, it's just getting used to a different one and missing some of the features I no longer have.
I want a good 1/4" on both sides of the needle (plus a hatch mark across the foot to show the 1/4" in front of the needle) so I don't have to draw seam lines when I'm doing these what I still call "modern strip piecing techniques" as opposed to putting together one piece at a time. If you don't have one, you should probably draw the seam lines when sewing to the left instead of to the right as usual.