Jim, it seems to me you want specific questions without defining (other than 'depression era') what the actual financial picture looks like. Each course could be at a different place in a downward spiral, therefore the actions taken in your questions would all be variable to the specific financial picture of that course. One course could be slightly down with a regional demographic and core golfer demographic vastly different (even in a depression) than another course.
Every one of your questions has a sliding scale of responses and degrees of cut-backs that can't just be juxtaposed against a vague or nebulous set of problems that it is only referred to as a depression era.
"1. When would you start changing items that impact architecture, grassing types, mowing patterns, maint practices, etc?"
When one starts to not break even or start loosing money at an unaccpetable rate... When is that?
"2. To what extent would you tweak? Consider bunkering, tees, greens, fairways, cart paths, carts, course supplies, amenities, and the like?"
To the extent that the budget VS revenue or sales can be brought back up with the extent required to make the difference to turn it around or hold on at even. What extent is that?
"3. When would you consider changing mowing heights, converting bent to blue or, in the case of the north letting bent go to poa?"
When the budget or balance sheet turns negative and enough to at least break even. when is that?
"4. When would you go change fairway and tee dimensions? Or even close selected tees? Fill bunkers or more? What would you replace them with?"
When the balance sheet goes negative and needs to at least be brought even. Do what it takes to get that done. What will it take when? How bad off are the numbers?
There just isn't a specific answer... I don't think.