The last DONE4 I had re-issued (added two new segments and changed dates of remaining 3 segments) was by BA at LHR T4 and took no more than 10 mins and no charge. I was surprised as I handed over the credit card and was told there was no charge. But this was about 2 years ago.

Its always better to have the issuing airline to the re-issue if you possibly can. Not always possible when you are part way through a journey.