I did a little research on this topic because I'm also interested in sail repair. We have a very old, very worn out mainsail and my husband is determined to get a new one. Our sail has at least 20 patches on it and is the wrong size. At the end of our first season, one of the mast track slugs got caught halfway down the mast. My brother, with the go-ahead from the captain, gave it a tug and ripped a hole through the sail, around the ring, and the luff rope. I patched it using sail tape and sewed it with my home machine and a denim needle. I used the zigzag stitch because that's how all the other patches were sewn. The only trouble I had was after sewing several inches, the needle would get sticky from the tape and I would have to clean it off to keep sewing. It worked though and we used the sail all last season.
I would think that a straight stitch over sail tape would work ok as a straight stitch is actually stronger then a zigzag, it just doesn't have as much stretch. If you set your stitch length as long as it would go, that might alleviate some of the problem. Be sure you use strong thread.
Here's what info I could find searching the web:
Sailmakers use a zigzag - which is also called the "sailmakers' stitch" partly because sails are subject to a lot of wind shock causing the seams of bias cut fabric to stretch, and partly because it is easy to rip out zigzag stitches when a seam needs adjustment during manufacture as it often does. On thin fabrics a zigzag stitch reduces the risks of running tear failures (fatigue induced failures)