I have the same problem. I bought one of those travelling sprinklers
for $70. That's alot of money for a sprinkler. It's supposed to
cover a 60' diameter for 45psi, but I only get half that coverage.

I have well water, so I called the "water guy" to check it out.
He checked the intake on the iron filter, and it was almost totally
clogged. He replaced it with an intake that had more holes/slots, and
he said that I would see a huge difference in water pressure.

But I haven't.

I really want to have a nice lawn this year, and water will be
critical, so I'd really like to get the pressure up. But I have no
idea what to do next.

The pressure guage on the water system is set for 40/60, so there is
obviously a serious pressure drop from there to the faucet.