II had the same problem.
You are right the problem seems to be related to DETE
The install log seems to indicate it wants to do a reboot, but it doesn't.
I can't remember the command, you can generate form looking in install log.
But basically I ran the MS installer, in full interaction mode, on the DETE I did a repair and install.
I may have rebooted,
Then when I reinstalled Studio it worked.
So get DETE installed correctly, then Studio should install okay