Unlike some other commenters, I think that from-scratch rewrites can be valuable. But seriously consider other potential benefits. "Julia might be nicer than Rust" is not good enough if sole justification.
Yeah you can call Rust from Julia.
Rewriting seems like a pain in the ass, especially because Rust isn't causing your current implementation problems.
Generally I suggest avoiding rewrites; Usually the ROI is not there (see the strangler pattern for an alternative). It might make sense to look at Julia for future development. You could write something new in Julia to see if the benefits are there for your team. Also, from my understanding you can call Rust from Julia using extern in Rust to pretend to be C. It could act as an escape hatch for performance issues if there are encountered, though I have never tried it.