Yes, backward compatibility is a must. I want to be able to move from 4.1.4 to 4.1.5 without any hassle!
I am 100% in favor of fixing these broken signatures. BUT - please schedule a separate release ONLY for this - don't roll this into a release with myriad of other things that may or may not break. Land a final 4.1.x release and then make a 4.2.0 (or 5.0.0 if that's what the CI Charter stipulates) with all these signature changes and only these changes!
You will then have a 4.1.x branch for important bug fixes (supported, say 3 months) and us users may test and migrate to 4.2.0 (or 5.0.0)