So the water is coming *out* of the overflow via 1" pipe?
It sounds like the pipe isn't large enough and you're getting air trapped in the pipe which is inhibiting the increased flow. Couple of things to try
Although the diagram is for a larger pipe the principal is the same. Although you'll probably find the vent to be a bit noisy as well.
I would check the way the 1" pipe is setup and redo it so its either close to vertical or if its angled to have the angle in as straight of a line as possible.
You can see a *muffler* for one of these vents in my book pg 191