Clean install/add OS to clean HD

Once you've installed one of the cloning apps, open Disk utility (Applications > Utilities), highlight your internal drive and erase it, name it Macintosh HD, and format Mac OS Extended (Journaled) with GUID partition scheme to make it bootable. Then launch the cloning app and select all to clone to your internal.

Hopefully that should work.

If I understand this correctly, you can boot from your USB drive? Then I would just use CaronCopyCloner or SuperDuper to clone your system back to your internal drive from the USB. install one of those two apps on your flash drive and then clone your system.

Do you have a bootable El Capitan on the USB drive?

https://support.apple.com/en-us/HT201372

And what does it do if you put in the Password?

you are welcome!