Dear Elise Anderson, yes there is hope to remove the mineral volcanos that are erupting from the water channel outlet holes under the rim of your toilet.
I agree that you probably cannot get the proper angles under the rim if you use a hard pumice stone. That is why I use a soft pool-tile pumice stone from the pool store. You will know if it is a soft pumice stone by its weight. The big block should be really light weight.
You soak the pumice stone in water for at least 15 minutes before use. Then as you scrub with it under the rim - the stone starts to conform to the shape of the rim as parts of it are abraded away. It's not a cheap pumice stone but it is very versatile in the house as well as in the pool.
Next, you use fine grit emery cloth or sandpaper. Roll pieces into small tubes that will fit into the holes beneath the rim. Insert the sand paper into the holes and twist it back and forth to remove the deposits in the holes. It won't take as long as you think. The results will be amazing for the rim and use the same pumice stone on your toilet bowl.
Now for the bad news. If you have mineral volcanos that are coming out of your water channel holes, then there is a good chance that a lot of that crud is coming from your Toilet's Tank. That's another cleaning job.
The good news is I am in the midst of publishing a Post for that exact tough cleaning job - so follow me.
Also, check out all of my cleaning tips for difficult bathroom cleaning problems at: https://www.selfcleen/pages/cleaning-tips
Good luck, Matthew