Can't install game due to previous digital download

So last year, I bought Deus Ex Human Revolution on the marketplace, which was fine but then a few months later I won a copy of the Directors Cut version. The problem is I can't install either of the DC version's disks because the Xbox thinks I already have
the game and so the game runs of the disk (which is really loud) and has really long load in comparison to when I was playing off the HDD. But if play the digital version I can't access any of the extra content from the DC version. Is there any sort of solution
to this? Is there some way I can install the DC version?

Things I have already tried:

1. Doesn't matter if the digital version is downloaded or not

2. Signing out, disconnecting from Live

Would I be able to do it if I factory reset then install it first chance I get before downloading my profile again?

:)

 

Backwards Compatibility

BC games do not install from the disc, but are downloaded digitally from the store.

Is this a disc or previous digital download for the 360?

 

Just joined the Xbox One Family Thank You Phil Spencer

Whats people opinion on these game install times.

Assassins Creed Unity Digital Download took 1hr 23mins to install to 100%. Since Unity is a Digital Download will that included the latest patch or will that prompt to install once I run the Game.

Assassins Creed 4 Digital Download took 48mins to install to 100%.

So I take it these games install while downloading at the same time. I thought I would be download the files then it would extract them to install, similar to demos on the PS3.

Dead Rising 3 Blu-Ray Disc install took 26mins to install.

 

Instead of doing a factory reset try deleting the game, then clear the console's cache and finally restart the console.

Then try installing the game from the disc. If that doesn't work then try signing out of your gamertag and install the game then.