Hi,
After wiping the drive and formatting it as MBR... Did you use the specific UEFI or Legacy flash drive ?
Very Important...
There are no drivers needed for what you are attempting to do... Anything needed would be included in the Windows 10 installation media... Whether HDD or SSD...
The only reason my one installation required drivers was that there were no drivers available for that type of device included with windows...
There is no way it could be configured to not be a boot device because of some previous use...
Unless the HDD was plugged in at the same time maybe...
What you see in the way of drive letters within windows has nothing to do with a installation... Especially after the drive was wiped...
In reality, if you were to have a problem installing windows to the SSD, that should happen with UEFI, not the Legacy... You might double check that your Bios does in fact switch to Legacy when attempting a Legacy installation...
I'm thinking that there is a problem with the SSD's internal controller that it is not being recognized properly...
Just a thought... You might try plugging it in to a different SATA port on the motherboard just to see if it makes a difference...