After carrying this in my pocket for a few days, my thoughts so far:

• Sliding a straw over the tape as a sheath hasn't proved necessary so far. Doing so would add bulk, making the deployment of adjacent tools difficult or requiring a reduction in the amount of tape stored on the bit driver.

• The thick gorilla tape makes it impossible to open the adjacent pliers without first opening the bit driver because the pivot point of the pliers sticks out. Putting the thicker tape closer to the bit (swapping positions of the painter's tape and gorilla tape) may alleviate this, though I'll have to try it to confirm. Otherwise, I'll have to reduce the amount of tape stored lower on the bit driver.