...Am I wrong to assume that the adjustment screw will reduce the pressure to the desired levels?
I'm going to say yes... sort of... at least technically... (on the wording)...
The purpose of the adjustment screw isn't to "reduce the pressure at the head". Its purpose is to adjust how the head reacts to various pressures. So when "1800 literature says it takes an inlet pressure of 15-70psi", that means that the device will function within these pressure ranges. Less than 15psi and the head likely will not popup. More than 70psi and you're likely to start damaging the device. What you really need to look at is the specs for the nozzle. It will tell you approximately how far the nozzle with throw water at various pressures AT THE NOZZLE assuming the adjustment screw is fully open. So an example spec for a nozzle might be 15' @ 60psi, 12' @ 30psi, and the adjustment screw can reduce that by 30%. For this situation, it would mean that if you have 60psi at the nozzle, the water will throw from 10'-15' depending upon the adjustment screw, but at 30psi, it will throw from 8'-12'.
Todd is correct that a way to regulate the pressure on a zone is to use valves with flow control. Basically that is just a valve with a screw that is used to restrict the water flow (by restricting the water flow, you reduce the pressure... a pressure regulator uses the exact sample principle, but it opens and closes the restriction so that the exit pressure remains constant). Pressure regulators for the entire system usually are not used unless you have a starting pressure of something greater than 80psi. Then to protect the system, you install a pressure regulator at the point of mainline connection to reduce damage to the system from excessive pressures.
If you try to go the path of using flow control to adjust the pressure, changes to the input pressure (such as changes in local water demand if you are on city water) will effect the pressure at the nozzle and hence the throw of the spray heads. So rather than trying to tweek pressure with flow control alone, I personally decided to purchase the 1800s with the pressure regulator built into the pop up and valves with flow control. That way, I only had to design my system to insure I was getting about 35psi at the pop-ups, I can still use the flow control on my valves to make gross pressure adjustment, and I don't suffer major effects from pressure losses in lateral lines since the pressure reaching each nozzle is about 30psi.
The other thing to using the pressure regulators in the 1800s is that you will have less flow at each nozzle. Water pressure not only affects the distance the water is thrown by the nozzle but also the flow rate at the nozzle. So if all the heads are spraying at 30psi, your flow will be lower than if they were spraying at 50psi. After all, it sounds like you're designing this system sort of blind because you don't really know what the maximum flow rate is. (You've measured using the bucket test at a hose bibb not at the point of connection, and you're ASSUMING you'll gain 3gpm between your test spot and your actual connection). You'll do much better as designing a little more conservatively. As a suggestion, you might want to consider using the MPRotators in the 1800s. They will use much less GPM than spray heads. They are more expensive than nozzles, but you can also design head placements at 15-20 foot spacing rather than 12-15 foot spacing for typical nozzles.