>>> So now we have two cases that require fixing perform-replace.
>>
>> To be able to redesign the match-again part of perform-replace,
>> there is a need to have a test suite that will confirm nothing
>> is broken after redesign.  So I pushed a new test in replace-tests.el.
>
> The need to have `looking-at` in `perform-replace` is explained
> in the commit message of 5632eb272c7.  So now added it to replace-tests.

The only way to fix all reported problems is to always use
search functions in perform-replace: