A quick touch with a dry, hot iron helps as well. It sets the glue nicely. To avoid glue on your iron, press using parchment or freezer paper.
I drizzle in a grid pattern and don't feel it needs spreading except at the edges or if I overdo an area. I work approx. a third of the length and the whole width at a time. Like you, I use Elmer's washable school glue.