I've read a lot about homebrewers shaking a keg to carbonate at 30 psi, but risking overcarbonation.
Why not just shake the keg at 12 psi (and 38ish degrees). It might take a bit longer, but much less risk of overcarbonating, no?
Anybody tried this method?
it will take 3 times as long to carb up as shaking at 36 psi.
Since the shaking is aimed at speeding up the carbonation, and the big uncertainty is how much more contact area you are actually creating and for how long, while shaking, I don't see much advantage of shaking at 12 psi vs. just leaving it alone for ~24 hours at 36 psi and then dialing back to 12 psi.
Shaking at high pressure for a few minutes accelerates CO2 adsorption so you can serve a semi-carbonated beer within perhaps a few hours, or better yet a day or so, if you guess it right. Or you could over-carb it. You are trying to aim at something like "75% of CO2 from shaking, then 25% from slow carbonation over the next few days". Sometimes you overshoot or undershoot, and end up with overcarbed beer or beer that takes longer to carb.
Shaking at low pressure doesn't quite get you there right away, but still has uncertainty associated with shaking. Plus the strain on your back. So it's more like "25% from shaking and then 75% over long term".
Burst-Carbing gives you all the control you need and will get there in a day or two. It's similar to the shaking part, except burst takes place of shaking and is much better controlled. So first 24 hour or so gives you 75% and then 25% from slow carbonation at serving pressure. It gets you to your CO2 pressure in much more reliable way with only a small delay in time compared to somewhat unreliable "shake at high pressure" method, and faster and more reliably than "shake at low pressure method".