How early is "early am"?
The prevailing wisdom is to have all watering done before sunrise, and not to water EVER in the evening (you're setting yourself up for fungus).
Try starting your watering cycle at midnight or shortly thereafter.
There are booster pumps available for city-water systems, although most water companies discourage or even try to prohibit their use. Consult your local irrigation supply for proper pump sizing if the timing thing doesn't work out.

You might want to check your gpm and pressure during peak times so you know not to exceed it.

I do agree with waterit you need to water during the wee hours in the morning or look into the mp rotator nozzles by Hunter they do perform at lower psi.

Here is a link that might be useful: do_it_your_self_web_site