There is no such thing as too much starch--LOL! I can think of several reasons why your blocks are shedding threads. Can you post a picture of the back of the block?
1st idea: I have more trouble with those cotton/poly mixes than any other type of fabric. They shed threads forever and as a new quilter, I seemed to have a bunch of those in my stash. I think they were cheap and I had planned to use them to make jumpers & shorts for my daughter when she was a toddler. She's 19 now but I still find some of those fabrics in my stash from time to time. I think I may have purchased some solids when I first started quilting also that I didn't check the content on. I still use them but you have to be careful ironing them because the heat will cause the poly threads to shrivel making everything all wonky. I don't worry so much about the threads shedding because the seam will usually stop that if you're seam allowances are at least a scant 1/4".
2nd idea: Are you sewing an accurate (straight) seam? When joining patches together--do you pin at the intersection? I hated to use pins and I still refuse to run my machine over them but I found that some fabrics just will not nestle & lock together like all the gurus on tv say they will so I still stick a pin straight down through the intersecting seam & make sure it matches up before sewing. I have even run a basting stitch to make sure everything lines up before making my real seam & I still check to make sure if something just doesn't feel right.
3rd idea: Are you running really long strips through the machine and then trying to sub-cut those down into units? I still get sloppy with really long seams and let my seam allowance wander unless I force myself to stop and check every 8" or so.
4th idea: Are you sure you're not pinching some fabric into the seam line when you press? I press the back & front of my blocks as a double-check.