I attach it and allow it to be controlled through Virtual Box (does that count as raw attachment?)
A 'raw' attachment is when the virtual OS has direct access to the hardware without using an additional layer (form the virtual environment, such as Virtual-Box) to access it.
To answer the question: no you seem to be using non-raw mode for your USB device.
Just make sure the VM is not using USB 3.x, and in case USB 2.x also gives you issues then let the VM fall back to USB 1.x.
Mine's an 8GB USB 2 stick and tried to install as 4GB for OS and 3GB for work partition
If you are doing a full install then those sizes (especially the size of the OS partition) seem to the the cause of your issue(s).
The installment is the 2.54GB Icarus Live!
2.54GB is first copied onto your USB device, then extracted (so roughly 2.54GB * 2) which (last time I checked my match skills) is bigger than 4GB
Should I go for the smaller non-Live version?
Unfortunately my memory is a bit lacking there. I can't remember if all the archives are copied to the USB device first and then those selected would be extracted _or_ that only the selected packages would be copied first and then extracted (I seem to remember that Paolone made some changes to that part of the installation process over the years)
In case the latter then you could also try not selecting all packages but only those that you are interested in. It would be trial and error, unless someone that knows informs you about it.
If your use case is mainly because you wish to try out running Icaros as an installed OS from a USB device then perhaps using the smaller version would be easier to setup for you (

. But in case you do have a USB device with a bigger storage capacity then you could opt for that as well.
fwiw: the installation process is unable to detect the situation you ran into properly and tries to keep on going indefinitely, despite that the filesystem is already screwed up somewhere during the installation process. Somehow we never managed to be able to properly catch this error and be able to inform the user about that in a more proper way.
edit (*): If i recall correctly then a 4Gb OS partition size was also not enough for the CD version of Icaros to be able to install correctly. It was pretty close, so you might be able to get away with it.