Just to check is /wrkdirs a tmpfs or a regular directory on disk? If it is a tmpfs this error makes sense. Rustc needs more than 12GB of disk space to do a full build. If not I'm surprised it is rustdoc that fails. I would have expected rustc_middle to need more RAM.
Then that is the issue. The wrkdir got so big that there is no memory remaining to run rustc. You will need to disable tmpfs usage for the rust port. According to Solved - tmpfs for building ports | The FreeBSD Forums there is a TMPFS_BLACKLIST option you can set together with TMPFS_BLACKLIST_TMPDIR. In fact the example usage for this option shows disabling tmpfs for the rust port.
I don't think you can without patching the build system of rust. And even if you did, doing so would break cargo test as it will use rustdoc to run doctests. And finally disabling rustdoc would almost certainly still result in an OOM once it goes building cargo.