Jord,

Check your water pressure from the spigot. I believe your problem might stem from too high a pressure in your house. You can buy an inexpensive pressure gauge that screws on to your hose faucet from the hardware store. Let us know the pressure reading. Aloha

I remember the home inspector telling us it was I think 60-65 psi when we bought the home 3 years ago.

What should the water pressure be for a typical 1 story 1600 sq ft house?

A water hammer is especially likely when there's a long column of water behind a dead end valve, so the long run to a yard faucet probably qualifies because there is all that water trying to come to a sudden stop. I suspect your problem is that you're essentially slamming four faucets closed at once, which is almost certain to hammer. Consider getting away from all four valve closing together and use multiple single timers set to different times, which would result in a much smaller flow coming to a sudden stop. I would definitely try letting it shut down with only one hose and see if it hammers. I suspect it will not.

Jord,

A typical residence should be regulated to 55 psi pressure. Most water using appliances and faucets in your house wear faster with higher pressure. 60-65 psi is not that extreme but the house pressure regulator may have failed. Check your pressure at an outdoor faucet with an inexpensive pressure gauge. The gauge fits on the faucet with a hose type fitting and can be found at any hardware store.
Gerald is exactly right and it is the higher pressure that really get the mass of water moving in the pipe only to bang against a fast closing valve gate. JMHO Aloha