But as soon as I acknowledge an obligation to help people I have never met, there is nowhere I can stop and still feel decent.

Living with this constant moral pressure is unlikely to make you most effective. A better alternative is to budget your money in advance, and give yourself a modest amount that you are free to use as you please. Jeff Kaufman's Keeping Choices Donation Neutral argues for an approach along these lines. If I remember correctly, Toby Ord makes a similar point in an early unpublished essay.