Unfortunately, I'm not finding the numbers I need to get a good estimate. The important question is what portion of petroleum use winds up servicing those poor people versus the rest of the economy, because while it is certainly true that a small percentage increase in the costs of necessities hurts these people disproportionately, the money returned is a much greater portion of their income, and could very well dwarf the increased costs (indeed, this is what I would expect).

The very worst case, of course, is any who find themselves paying higher prices but unable for whatever reason to access the stipend.

Why? The average person will come out exactly neutral. Use less petrol than the average, and you come out ahead. Use more, and you are a net payer.

Transporting stuff doesn't need to use all that much oil. Neither does growing.