All I can offer without going into the weeds is that it is not the shape of the paths, but mearly the relative length of two paths though spacetime that matters.

Proper time and proper acceleration is possibly a pathway in flat spacetime?

Learning that the order, timing, and sometimes causality of events is also relative tends to be a barrier, thus some of these didactic half truths are useful.

The "Einstein train paradox" is the classic intro to the relativity of simultaneity if you aren't familiar.

In the SR case, proper acceleration is possibly the better option.