I think it’s common to revert to shapes that work and that you are familiar with. And, really: if it ain’t broke, don’t fix it!
But, I understand where you are coming from and that you want to broaden your palette.
First, my own fallback shape is an extension of yours, the “funk box” (includes your notes and additionally the fourth and the minor seventh) - works with almost all rock, funk etc.
Check out Josh’s video on this here: Beginner Funk Bass Made Simple (Bootsy’s Funk Formula)
And then, a further extension of the funk box is basically using pentatonics over a larger range. Whenever I want to explore a bit more of the fretboard for a fill etc, I use this shape (boxed in in red):
A good way to (slowly) get away from only playing one’s preferred shapes is to copy what others have done and try to incorporate that into your playing. What you will notice in a lot of rock, funk etc is that there is pentatonics everywhere. Still, there are many different pentatonics licks that you can learn and then incorporate.