Not trying to overcomplicate things here, but two suggestions:
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If you elect to use a pet operator, can you set some parameter like the operator can only pet the gotchi after you are late by X minutes. So user has option to still pet their own gotchi, but if they forget and the time threshold passes, it’s fair game for their operator to pet it and they get charged the GHST fee.
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Would you consider allowing a wallet address which owns at least one gotchi to be able to have one mutual “Best Fren”, which is another wallet owner that must have at least one gotchi. If the two parties agree to be each others “Best Frens” then either of them can pet each others gotchis (up to 10) at no no charge. There would be a cooldown period of 3-7 days to change your BestFren to avoid abuse. Either wallet holder could dissolve the Best Frenship, but both wallet holders must opt-in to the Best Frenship.