I find it to be really annoying and counterproductive to have to start a new save, and go all the way through a questline just to test out some updates to my mod. Is there really nothing we can do about this? It's the only way I'm able to get changes to quests to show.

You could use setstage and coc to speed things along.

The Dark Brotherhood quest stages are so filled with crap that setstage is a near impossibility. Things don't update properly and it's just a mess.

Lost and lots of saving as you play so you have save points at various stages of the game, minimizing the work you need to do to test something. There is just no other practical way.