Ray Tracing with Cones: coverage, overlapping and abutting triangles
I did implement a ray tracer based on Amantides' work but, as that was  years ago, my memory of the paper is a little rusty.

However, ignoring this particular case, in general when it comes to working with fractional coverage e.g. Alpha compositing, (see "A over B") my understanding is that the usual assumption is that the items being composited are uncorrelated.

Thus if A with X% coverage is on top of B with Y% coverage and C in the background, then it's assumed that one will see
    X%*A + (100-X%)*Y% * B + (100-X%)(100-Y%)*C

Does that make sense? Obviously this will give "leaks" in the case where A and B are strongly correlated.

I think I might have put a small bit mask on the rays to avoid these problems, but it was a very long time ago.