Doodler,
Changing a messy diaper in a public restroom is a "challenge" and not for the faint-of-heart. Of course, it can be a character-building experience.
It sounds like you are handling the emotional side of incontinence very well.
Rushing to take a diaper off too quickly when you are just about to have a bowel accident is a risky step. There is the danger of an accident while your diaper is halfway down and thus soiling your clothing.

It is safer to just complete the void in your diaper. Of course, if you have more warning and do not have to rush, I would remove the diaper and use the toilet.
This will sound strange, but, after your next bowel accident at home, try changing the messy diaper at your toilet just as you would have to in a public restroom. This will give you a safe and private place to practice to find out what works best for you.
--John
(old enough to be your grandfather)