The tax hikes and government aid to business did not really come until 1932, much closer to the bottom than the top. It is well worth nothing that the 90% top income tax bracket remained in place from 1932 until 1964, so it certainly did not prevent recovery from the Depression, nor did it cause the Depression. There are also scholarly reassessments of how much Smoot-Hawley actually contributed to the Depression.
It came towards the end of his presidency, but I'm not just referring to the top rate (although I personally have no doubts that does in inhibit productivity). Aside from raising the top rate from 25% to 63% he also reduced personal exemptions, increased corporate taxation, AND added a check tax.
There is considerable evidence that the money contractions of the early 30s were exacerbated by the latter policy alone.
Hoover's Emergency Committee on Employment (PECE) mobilized charity and encouraged local government to implement public works. While the federal government did not directly fund programs, the states did. The New Deal just went further on this by involving the Feds in the process under the assumption that it was a more effective use of resources. I'm not sure I would call that 'swamped.' Poorly implemented, perhaps.
As for unemployment: Yes, and he also attempted to bail out the banks under the Reconstruction Finance Corporation. Which just re-affirms what I said earlier.
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