The string should sit half way down in the nut slot. In other words, if more than half of the string sticks out, it can give you issues. If it doesn’t, I guess you don’t need to file it.
On TalkBass, a user wrote they used the strings themselves as files when they needed to file the slots.
Personally, I think 110 should be so close to standard 105/100s that it won’t matter. Show us a picture when you’ve strung up.
For C tuning, this might still be a bit floppy. I have 110, and tuning down to C really was very low tension, I didn’t like it. For the occasional downtuning to C I now use my bass whammy. As I play to myself in my room, it doesn’t matter that much that it doesn’t sound perfect.
Justin Chancellor uses a 110 E-string for Drop D, for Drop C he uses 135.
But just try it. You can still adapt if it doesn’t work out. Might then just as well be an excuse to get another bass
I can’t speak from personal experience, but I wonder if a set of DR Strings DDT could be of interest. However, you still need to choose the gauge, so your original issue is still relevant.
Recemtly aquired a cirrus BXP , also tried bigger strings for same reason, the string fit the nut after some convincing, but sits to high, off frets now. I left it as is because its a temporary experiment, also much harder to play faster , so it’s a fnger gym as well.