Thank you for your comments and encouragement!!
I am already doing many of the things suggested - overcutting, starching, pressing (not ironing), though I do admit to using steam.
There are two problems I notice I have - 1) my machine does not pull the fabric evenly. If I seam two pieces of fabric the exact same size, they often end up being off by a few threads. The top fabric is pushed "downwards further" than the bottom. I don't know if this is a quirk that is particular to my personal machine or all machines in general or somewhere in the middle. and 2) I use a quarter inch foot but because it is metal and not clear I can't see the last 3/8" as it is being sewn so often this part of my seam will be off, either too wide or too narrow by a couple threads. (And there was a third thing I thought of while writing this but it's gone from my brain, can't remember what it was.)
I know when I'm finished with a quilt I look at it and say that those little "offs" really aren't noticeable at all. It's just that when I'm trying so hard to have everything match up it's discouraging when I'm off by so much on every square.