I agree, rewriting with a clear head works wonders - but, to be fair to the op, when you rewrite your own code you'll be very appreciative of all the challenges and possibilities.

It's a very different kettle of fish to rewrite from scratch strange code you've not properly explored and given a chance to - which is the usual situation.

Knowing what the system should do, in sufficient detail that there is nothing of significance to be discovered with regard to its requirements, while simultaneously not actually knowing enough about how it works to the point where you could plan how to refactor it, is quite a corner case in the field of legacy systems (the latter is quite commonplace, but the former is almost unheard of.)

Rewriting a chunk is much easier than rewriting the whole application.

In fact rewriting a chunk sounds rather like refactoring.

Rewriting "a chunk" of code kind of is refactoring, though.

But rewriting one chunk at a time could be considered refactoring.