You should probably review the NIST guidelines, no need to randomize the data, just fill it with 0 & 1. NIST uses the word pseudorandom a lot.
Good summary:
https://www.bitraser.com/article/use-nist-hard-drive-erasure.php
Reference:
https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-88r1.pdf
Writing some strings in parallel might be a lot faster, I believe you have 8 channels on most controllers, so you can probably get 4-5 writes in parallel.
This is only true if you write sector by sector, the OS controls where that file is placed. You would have to write 1 file the size of the free space to make that true in your scenario.