It may be only a rhetorical question until or unless you recover and change your mind.
Your making this too complicated.
Did you install EasyBCD?
It will remove the entry for the drive E boot option and let you create one on Drive C.
It's easy to use, it's just a graphic way of editing the boot setup files, instead of doing it through the command window.
All you have to do is use Add New Entry to create a boot option for your Windows 10 install on C:\.
Move it to the top of the list and make sure it boots, then you can remove the second entry.
Windows won't try and boot to the E drive once the entry is removed from the list, but as long as it's there the computer won't boot if you remove the drive.
I found this out the hard way a long time ago.
Now when you look at your E: drive partition (system reserved partition) the hidden boot files will be visible:
My System Reserved partition has 311mb of boot files on it and it is sized to 350mb total, which is what a clean install of Windows 10 will create. I am not sure if the Recovery folder in mine is needed to boot or not - it's got some really tight permissions attached to it and the only way I could get into it was to make an image of the partition with Macrium Reflect Free, mount the image file and explore it that way :-)
Now, in the past, I have been able to set my C: drive partition as the active partition, delete the system reserved partition, and use the Macrium Reflect Free rescue disk to recreate the boot files on my C: drive partition. Maybe it is a limitation of your bios that is keeping that from succeeding with your computer, but it worked on mine, in the past with Windows 10.
Merely editing the system bcd store with EasyBCD will only change where the boot files point to to find the operating system, but it won't change where the actual bcd store is physically located - which will still be in the system reserved partition.
If you don't want to see the system reserved partition as a drive letter - just go into disk management in Windows and remove the drive letter from it. I normally don't have a drive letter assigned to mine.