some questions:
is your timeline full rendered?
is there some media in your timeline (around the halfway mark) that could be causing FCP to struggle, and crash?
I’m thinking large image files.
i has some rather large image files in a project a year or so ago,
and had the same problem, crashing on export.
even when they were rendered!
i took that section into another FCP project, which was much smaller and simpler,
and i was able to render and export from that one,
then i brought that new export into the original project, and laid it over the problem section,
and i was able to export again.
phew ☺
nick