Correction then: Obsidian are making the Fallout games these days. They may not feel like upholding Bethesda's promise.
That's false. Bethesda owns the franchise, they approached Obsidian to make New Vegas and they still plan on making Fallout games.
But anyway, I am fine with any time period, though this is my criteria:
1. There must be a sense of lawlessness (I think New Vegas was pretty adequate in this regard, it's a frontier land)
2. There must also be development (New Vegas was also good here, but perhaps too good. I would prefer a place without a large and developed nation)
3. It shouldn't be more that 20-30 years in the future
4. It shouldn't be right after the war (before Fallout 1, maybe.)
This can be achieved by many ways, not just setting back the timeline. We can have a new place with brand new lore such as the South, we can have a major dwindling of Caesar's Legion and/or NCR, we can have those governments lose competence, etc.