Had same exact issue AND SOLVED IT!
My problem was the "Microsoft SQL server 2016 LocalDB" was not getting downloaded and installed no matter what when I ran the EF install program. Then an "Error 12007" would pop up and when finishing the install and running EF it would make me reregister every time and never saved my settings!
I had to search and download and install Microsoft SQL server 2016 LocalDB then run the EF installer which finally showed Microsoft SQL server 2016 LocalDB as already installed and it skipped trying to download and install it.
Install went flawless after that!
I had my firewall, AV, and UAC disabled and ADMIN Privilege's active so it wasn't any of those causing the issue for me at least!
The EF installer seems to be having an issue with acquiring and installing the listed Microsoft file for some reason?
Order: MFBARRPGS Placed on 08/15/2019 18:21:08