You could eliminate those risky locations by excluding them as alternatives in your randomization process, but that would mean including a chain of reasoning!

Do I know that while I was trying to hide the coin I tought I would lose if I found it later?

Edit: Gwern said it first.

(You also don't formulate it right. If the memory-wiped self is told that finding the coin wins, and also that a former self placed the coin for him to find, wouldn't he infer that his former self would be trying to help him win and so would begin his search at a Schelling point? He wouldn't even consider trying to beat an adversarial strategy like 'randomize' because he doesn't think there's an adversary!)