I don't think it's the tension if you are happy with straight seams. It's just built into some machines that they tug a bit more in one direction or another and we have to work with the machine, or that we are working against the machine and not letting it do the work on a different machines! I also think that machine piecing requires hand/eye/motor skill coordination and some times we need to do a bit of warm up if our skills our rusty.
You might try ironing on a 1" strip of freezer paper on the back of one or both sides and pinning/sewing through it all. Quick rip off of the freezer paper when you are done.