I have two Japanese ZZ machines that park the needle to the left. One is a Dial 'N Sew high shank, the other a Domestic low shank. I found an off set straight stitch foot for the Dial 'N Sew at my LSMG and the Domestic came with attachment that included an off set SS foot.
Using these feet for straight stitching makes it much easier for me to get a consistently straight seam.
These feet are both wide enough to cover the feed dogs too.
Check with your LSMG for feet.
Joe