Hi Jen,
I've thought a lot about this, probably too much, so please excuse the long-winded explanation. There are a few ways to go about it.
What you've suggested is basically correct but the only problem with just opening the valve after setting the target pressure like you've suggested is that the regulator will be BLASTING co2 into the tank at high pressure/flow rate so most of that gas will rise through the cider straight to the headspace. In effect, you will charge the headspace with co2 first, and then co2 will eventually dissolve back into the cider. What this means is that early on your tank gauge isn't reflective of the cider because the whole tank hasn't reached equilibrium. If you wait long enough (24-48 hrs or so) then it will achieve equilibrium and it will be basically accurate. Either way, this is what the Zahm is for - measure the cider directly. Take a few readings along the way until it stops changing, then you're at equilibrium. Some folks like to charge the headspace through the CIP arm first to
about 1-2 psi below the target pressure. This can help the co2 dissolve
more quickly into the cider. Still not great though if your stone is
blasting co2 at high pressure and flow rate. In sum, this method works fine if you've got the time.
A better way to do it: Once you know your target pressure (based on the Zahm chart) then set your regulator to that psi (plus stone wetting pressure, 1-3psi, plus static liquid pressure - 1psi for every 28in of liquid above the stone). For example, if my cider is at 38 degrees, and my chart tells me I need 10psi to get desired volumes of co2, I set the regulator to 13psi). If you have a rotameter (measures flow rate) you can set the co2 to flow at 5-10 SCFH. At this low flow rate, the stone produces a gentle curtain of bubbles, which helps the co2 dissolve more efficiently into the cider due to the increased gas-to-liquid surface area of many fine bubbles. If you don't have a rotameter, a good way to approximate this low flow is to just barely crack the output valve of your regulator until you see the needle drop 5 psi or so - this restricts the flow, but the needle movement tells you the co2 has started flowing. Then you essentially just set it and forget it. The tank will slowly come up to equilbrium and stop carbonating at the target you've set. No need to worry about blowing the PRV or overcarbonating. This is my preferred way as we often flip our brite tanks daily and carbonate overnight and come back the next day, confirm with Zahm and you're ready to go. A little trial and error, plus some minor adjustments the next day can make this process very reliable if you have predictable cider temps.
Option two is set the regulator to something like 4 psi first and wait for the tank to come up to that pressure. Then turn the regulator up by 2psi increments and wait for equilibrium each time. Because of the small differential between regulator and tank, the co2 flows slowly, and the stone produces the fine curtain of bubbles. A little more babysitting, but largely passive. This works well if you're around to make the adjustments, you'll never overshoot.
Hope that helps.
Alex