I ran into the same problem where my original version of the BIOS was 1103 and I wanted to upgrade to the latest one at a time 4801. I saw all the same messages where in FlashBack option the lights would not start blinking and in the EZ-Flash it would not see the CAP files at all. There was one post which said I got it working it was the naming thing HOWEVER did not provide steps how. Anyhow after a few hours of trying different combinations I got it working, and here are the steps. Some steps might be pointless, however, I am listing what I did in order to get the 4801 successfully flash my BIOS.
1. Download 2002 version (Yes one right after ASUS made the change to CAP files)
https://www.asus.com/us/Motherboards/P9X79/HelpDesk_BIOS/
2. Download BIOS Renamer from BIOS-Utilities when selecting OS → Other instead of Windows 7/10…
https://www.asus.com/us/Motherboards/P9X…pDesk_Download/
3. Get a USB key and format it into FAT32 (possibly it doesn’t matter, but that’s what I did at that step)
4. Unzip the 2002 version of the BIOS into a temp folder on your computer
5. Unzip BIOS Renamer into the same folder
6. Run BIOS Renamer and press any key to complete the operation. You will notice it will create a new file with a shortened name. DO NOT RENAME IT, LEAVE IT AS IS.
7. Copy that file to USB Key.
8. Plug the USB key into the USB slot which is right beside the USB FLASH Back button on the motherboard
9. Shut down your computer.
10. Press and hold the USB Flash Back button until the blue LED starts blinking.
11. Let it blink for 3-5 minutes until it stops blinking, and only after that power up the PC.
12. You will notice that it will start Flashing BIOS at that point. Let it do its thing, which will require a re-start which it will do by itself and just wait until Windows boots.
13. Now download 4801.
14. Perform the same operation as was done in steps 4 -9.
15. This time power up your computer and go to BIOS EZ-Flash in Tools menu. You probably can do the same thing as in step 10, but I did it through BIOS to see if it can read the CAP files now.
16. Select the file from USB and do a read and program as all videos show on Youtube like on Gamers Nexus channel.
17. After successful flashing reboot and after completing the FLASH upgrade check your BIOS to verify that you are up to the latest version.
This was not too straight forward cause I could not get it to flash to 4803 directly, possibly I just had bad luck or missed a step but following the above sequence got me to upgrade. Hopefully this will help and save some debugging hell for you.
@valekiri - thanks for adding your tips for others. 
That is standard method to get converted from ROM to CAP BIOS, and then after that USB Flashback will work for you with CAP BIOS (Before you do that, you could only use flashback for the older ROM BIOS type)