The 1851 "no dots" halfpenny (P-1534) is much rarer than the 1851 "with dots" variety (P-1535). Since this major difference in die variety is not mentioned in the foregoing discussion, I assume that the recut letters referred to apply to the "with dots" die variety.
For the "no dots" variety, all specimens that I've ever seen are dated 1 over 1.
For the "with dots" variety, one has to bear in mind that re-punched letters or numerals are are common occurrences for all Victorian copper halfpennies.