recommmended sprinkler line pressure

I'm fixing my sprinklers. Our old service line was replaced with copper, and we replaced the pressure regulator for the house but the sprinkler taps off the incoming line at full city water pressure. (We did this on purpose so we could have high pressure to hoses and to the pool fill line -- although it can burst a weak hose if its fully pressurized). The sprinklers will turn on if I open the bleed valve (with or without power), and will remain on if I apply power to the solenoid and subsequently close the bleed valve. When I turn power off, the sprinklers shut off. But they will not turn on with just power to the solenoid. I could replace the solenoids with the original manual valves (which I saved) but this defeats the whole purpose of having automatic sprinklers. There are 4 sprinkler valves and they all behave this way, so I'm guessing there may be too much water pressure. If I put a regulator on the incoming sprinkler line, what is the recommended pressure setting? Or are there sprinkler valves that will work under higher pressure (I haven't measured it could be 100-150 psi)?

You might actually measure the pressures, rather than guess. You got any backflow preventer in the system?

Its definitely high pressure as I have burst two cheap hoses that I left pressurized, but I'll pick up some adapters to connect a pressure gauge
(1/8 npt to 1/2 inch pipe or hose bibb) and report back (edit -- its 70 psi).

here is a basically what my system looks like

(main line from city)
|
X(shutoff)
|
M(meter)
|
|
|
+----X----to pool fill line, hose bibb, sprinklers
|
+----X----regulator----+(to house)----x(pressure relief valve)

Note: All sprinkler and pool fill valves have built-in air gap backflow preventers, But no hose bibb has one, that I can see (Maybe this is a potential problem -- even though the bibbs are elevated well above ground level, any backflow could siphon back into the main line. There are anti-siphon devices available for these -- are they required, needed or desired?)

Was it a bad idea or illegal to have the sprinkler system on full city water pressure? (I could have a separate regulator added -- my next door neighbor is a plumber). edit -- no pressure regulator needed.

I asked the installer to install shutoff valves wherever they would be convenient to have. This was an inexpensive upgrade and I definitely recommend this for anyone replacing any large part of their plumbing.

If you want to run high pressure on the inlet, to be able to supply a large volume of sprinkler heads, you definitely need commercial rated valves. The typical homeowner valves at HD will not take over 80 psi. Find out what you have. Some commercial valves, like some better rainbirds, will take maybe 125. If you have more than that, you might need to put in a regulator./

Thanks for everyone's advice and suggestions. I've done a bit of digging around in the yard and on the web and here is an update.

My line pressure is 70 psi. My valves are old brass manual Champions converted to automatic with gray plastic Toro/LawnGenie actuators. The transformer is good, 25.2 volts under load. I bought a rainbird DAS/ASVF-075 anti siphon valve and tested it (test stand made of 3/4 pvc pipe). It works, so the old valve actuators are just not up to the job. But the rainbird makes a loud popping sound when it turns on - and a horrible very loud groan when it shuts down. Maybe its because I had nothing connected to the outlet -- but I can't stand the sound, so I will return it. I'm going to order Hunter ASV-075 valves online and hope they'll work out. I think this is the best solution overall.