I think I found the problem. When I was hooking up the pump, because of the pre-existing plumbing, apparently I installed the plunger valve in the wrong direction. I believe this was causing the vacuum release valve to suck in a lot of air. I am currently bypassing the plunger valve until I can get some plumbing parts to correct this.

Exactly what do you mean by this?
The new pump is moving a lot more water than the original pump and this is helping keep the pool cleaner. Also when vacuuming it actually sucks up whatever I go over the first time.

Is there air in the pump basket too?
There was air at the top of the pump basket but now that is gone.

If the pump is bigger and flow rates are higher, check the skimmer to make sure it isn't sucking any air.
This skimmer is staying full and is not sucking any air.

Does it only occur on start up?
It happened all of the time.

Do you have solar installed?
No

Is the equipment installed above or below water level?
Below