Several years ago, a friend used this alias, and I loved it, so I'm borrowing it to use here. The big misunderstanding with accurate 1/4" seams is that they really aren't 1/4" if they're going to result in a true block size--they're going to be a hair less than 1/4", to allow for the fabric taken up in a seam. I hope you all have seam guides for your sewing machines. Mary asked about this, and wondered why her 1/4" foot doesn't bring the desired perfection. So far, I've not found a foot that was accurate enough to suit me, which is why my machines all have a seam guide either in the drawer of the cabinet, or attached to the machine bed. If you don't have one, and the ones for your machine are very pricey, you can make do with a strip of moleskin or a stack of post-it notes, but I don't recommend that. I'm a great believer in using the right tool for the job at hand. Once you have one, the next step is to put a small clear ruler underneath your presser foot, and slowly bring the needle down until it just touches the right side of the little line on the ruler that indicates 1/4", so that it's just a hair less. I now have to wear reading glasses for this, which I deeply resent. Up until a couple of years ago, I could easily read and thread needles, now, not so much. :(
Next, gently lower the presser foot, making sure nothing moves. Place the seam guide so that it butts up against the ruler, again making sure nothing moves, and tighten it down. Remove the ruler. Then, cut 3 strips of fabric 1 1/2" wide, and sew them together. Press the seams to one side, and measure. If the piece doesn't measure exactly 3 1/2", readjust the seam guide and repeat with another 3 strips, until you attain perfection. When you have that right, you can go ahead and piece that block, and it should come out just right if you make sure that you have the top and bottom pieces aligned correctly with each other and that they are butted up against the seam guide. Give it a try, and see if it works for you. It's a little extra trouble, but so, so worth it when you don't have to deal with a 12 1/2" block that turns out to be 12 1/4" or 12 5/8".