Unable to Transfer Save due to Console

As the Topic Title reads, I’m unable to transfer my save to the Handsome Collection due to the XBox 360 being an amazing piece of hardware. Sarcasm aside, my XBox has aged pretty damn poorly, and can’t even run disks because the Disk Tray. Therefore, I can’t even simply reach the main menu of BL2 to upload my save, hell, I can’t even update the game.

Now, a simple answer here would be, why not just go to a friends house and use his XBox real quick? Well, all my friends are on the PS3/4. Another way would be, why not just buy the game on Demand? Well, I’d rather not spend $80 today for the Collection and BL2 just so I can use the main menu.

The last solution I’ve thought of was to simply go to my storage drive and directly upload to cloud, but I highly doubt that it would work. So, if anyone has any ideas that aren’t mentioned above, or recommends just playing a new character and restarting all 200+ hours, please speak up and thanks in advance.