Just avoid the double whammy. The Dust Bowl struck smack dab in the middle of the Great Depression, which is almost an ASB-level of bad luck, but sometimes real life is that way, too.
As I understand it, the keynesian approach focuses on GDP as the single most important number. And comparing the most recently measured period to that a year previously. And we ideally want 2 to 3% growth for a modern, industrial economy. And when it's negative, when we're actually producing less goods and services than we did a year ago, that's real bad. If various markets are not indirectly responding, we can do so directly, for example, through infrastructure spending. Although one problem is that it's hard to find enough projects to do the overall spending we need to be doing. And then once the economy picks up and things get tight again (such as genuine shortages of labor and interest rates being bid up), the governmental spending can be phased down.
But since the economy is almost biologically complex, I say clearly the way to do it is through a series of medium-scale experiments with rapid-cycle feedback. I mean, hopefully within a matter of weeks. Don't wait too long until the economy gets really bad.
The most important number in classical Keynesianism is aggregate demand (AD, or Y, total income), not GDP. GDP as a figure hadn't been invented yet, the closest in use was GNP, which lacks measurements of exports. The people who make extensive use of (nominal) GDP are the market monetarists, a decidedly modern approach.
The thing is, the assumption that Keynesian economics is some kind of magic pill (like you are treating it here -- seriously man, economics isn't medicine) is badly flawed. There is continuing controversy over whether the fiscal multiplier is greater than one and the concept of monetary offset is pretty entrenched, although a 1930's Fed isn't necessarily going to be as attentive as the modern day System.
More broadly, your idea of short turnover ('weeks') is hopelessly unrealistic. Quick-feedback macroeconomic statistics are collected and calculated
quarterly these days, with all the advantages of modern information systems. National income accounting didn't even exist in the 1930's (and wouldn't until the 40's and 50's), let alone
weekly. Even with modern access to statistics, there is broad disagreement over the exact meaning they have vis monetary and fiscal policy, because it's almost impossible to disentangle the effects of shifts in these policy regimes from the rest of the economy (ceteris is not paribus). So, there's nothing at all like a reliable, scientific approach.
The reason I brought up Benjamin Strong is because he was a man who had something that looked like a solution/best practice for the monetary authority that
already existed instead of trying to advance understanding of macroeconomics by
decades on a whim. He really is your best bet both because the modern understanding of the role of the Fed in the monetary contraction is that it was
central in the depth and length of the Depression and, having an active Federal Reserve that
actually does the job it was created for will head off the entire thing.
Including things like preventing the Smoot-Hawley from spiraling out into a general trade war helps prevent a lot of the real shocks that brought the financial system to its knees over the course of 1930 and 1931 which, in cooperation with an effective monetary policy from the Fed, can turn the whole debacle at the end of the 20's and beginning of the 30's into a minor recession that isn't any better remembered than the ones in '24 and '26.