Re: New line doesn't fit reel... how would you proceed?
I use to fish small streams and creeks with a 6 1/2' Orvis Superfine bamboo rod with a Hardy Flyweight reel. I always cut the double taper line in half and saved one side so when the half I was using wore out I could switch to the new line. It worked just fine and I even put on a little backing just to fill the reel. I don't ever recall casting all the line out or having a trout take me to the backing but then, as I said, I was fishing small water. It certainly wasn't a tarpon rig, LOL, but lots of fun.
A few other thoughts; a weight forward takes up a lot less space than a double taper. Because lines are so much better these days, I'd probably get a light reel that would fit the entire line. Lastly, cutting off a portion of the line so it fit the reel would be okay and not require any further purchases.