Well you don't really have to. How it usually works is the 2.5" part is used to connect to a long tube short system (Long tubes and midpipe) both ARH and Kooks offer them and they have a 2.5" taper as well.
You could cut off the 2.5" taper on both the cat back system and the midpipe from the headers system and weld in a 3" intermediate pipe. But I'm not sure how much is to be gained from doing that. The Flowmasters will straight up bolt on to both those short systems I mentioned.
I have just the cat back currently but when I put on headers I'll just leave the 2.5" little choke point since I don't really think it is choking the system all that much.
Post some videos when you get done
EDIT: Just reread your post and realized you already have a header system with a 3" end. In that case, cutting and welding would be a good option. Don't know which header system you have but you might need a little extra 3" piping to fill the gap.