White is so notorious for showing seams. That's why I stick with Kona white and lights. Really helps with this problem.
What you can do with your current situation is to back each block with fusible interfacing. I've used the lighter weight of the fusible interfacings to solve exactly this problem, but do a "test block" first to make sure what you pick out will do the job. Would be great if you had some "extra" interfacings lying around to test on the blocks.
I've tried just lining the top in the past. I haven't found it to be effective, especially if my batting is already white. The only time it really worked was when I used a white sheet, and then tacked it down everywhere, so the sheet was held tightly against the top. It wasn't working otherwise. Just a word of warning, if you're planning to FMQ this quilt, the sheet makes it a bit harder to quilt, and you should go through more than 1 needle because the sheet is woven to tightly, it will dull your needle. But I did FMQ mine, so don't let it deter you!