Where are all your threads coming from???
If you will use a "starty/stoppy" there should be nothing but tiny thread tails that shouldn't be an issue!
These are just little scraps of fabric that you start your stitching line on before you sew your seams, then sew off onto at the end of the seam. When you cut off the starty/stoppy you have no more excess thread than between pieces that are sewn assembly-line style. All the long bothersome threads are on the starty/stoppies!
You can see the "starty" behind the pieces that I'm sewing together. I find that Alex's 4-in-1 tool is fabulous for cutting the threads when I'm just doing single seams instead of chain piecing. The long thread tails that you can see on a previous seam is about the longest I ever have left on my piecing, and that is just because I was careless. I can't imagine spending 2 days trimming threads!
Try it! You'll like it!