I don't have time to explore this topic in depth right now (way too much on my plate already, and I'm not that fast or brilliant), but I suspect there's literature on this topic. Something I could find is this:
https://en.wikipedia.org/wiki/Firewall_(physics)
Basically, my intuition is more or less in line with this firewall phenomenon and that no particle crosses a true event horizon, even in their own frame, and no certainly no singularity.