Thank you! I managed to boot from one of the problematic USB keys.
In case someone else is facing similar issues my solution was:
- Format the USB stick with Rufus - as Suggested by @JonathanM (I used the settings shown in the attached screenshot)
- I took backup of my current, working USB drive (Using the Unraid WebUI: Main -> Flash -> Flash backup)
- I copied the files from the backup zip file onto the new drive without overwriting anything on the new drive (there were some file generated by Rufus after the format)
Thanks again for the help!