I don't think there's a way to guarantee that sendfile() won't block on Linux. On FreeBSD, you can specify a "go as much as you can without blocking, and then return" flag; Linux doesn't have a flags parameter for sendfile() (maybe it needs a sendfile2() syscall with that?).
You can maybe use readahead() and keep the file open, but that may also block as it does its work behind the scenes. A thread just for this kind of blocking calls would be nice. But even then, this doesn't seem sufficient; so you might want to use multiplex sendfile() calls in bursts.
Also, yeah, Linux aio syscalls are interesting, but they're quite tricky to use and not very portable. I'll check out your project, thanks for linking to it -- should be useful reading material while I learn Rust.