Since EFS is just an NFS mount, I wonder if you could do this yourself by attaching an NVMe volume to your instance and setting up something like cachefilesd on the NFS mount, pointed to the NVMe.
Would
mkfs.ext4 /dev/nvme0n1 && \
mount /dev/nvme0n1 /var/cache/fscache && \
mount -t s3files -o fsc fs-0aa860d05df9afdfe:/ /home/ec2-user/s3files
work out of the box? It does for EFS. It hardly seems worth it to offer a managed service that's effectively three shell commands, but this is AWS we're talking about.