Would a different gold parity have avoided deflation?

Could deflation have been avoided by restoring the gold standard at the contemporary market price?

No, in this interpretation: a different starting price would still leave the currency tied to subsequent changes in gold's value.

The question proposes returning to gold at the contemporary market price instead of the old parity. The answer rejects that as a way to remove the underlying problem. Its explanation concentrates on the currency remaining tied to gold and therefore exposed to changes in gold supply and market value. A new gold strike illustrates the argument: additional supply could reduce gold's value and weaken a currency pegged to it. The exchange does not quantify the difference that another starting parity would have made.