[XY] [ORAS] Restoring saves from Powersaves bin?

[Silveraith]

In 2016, I tragically lost my copies of both X and Alpha Sapphire, which had most of my entire accumulated collection transferred to them. However, I have backups that were made when I edited them using Powersaves. It's my understanding that these backups are encrypted to those specific cartridges or something like that, but the whole issue here is that I no longer have those original cartridges. What I do have is:

The Powersaves device and software

a N3DSXL at the latest system version with CFW

Digital copies of both games, though if need be I can borrow cartridges

My goal is to restore these saves so I can rescue as much of my collection as I can, because these pokemon date back almost 20 years. If anyone can help me in any way, be it information or action, I would be eternally grateful. I've attached a zip of the 10 save backups that were automatically created in my history of using Powersaves.

Powersaves3DS.zip

[Kaphotics]

Powersaves backups are raw rips from the cartridge.

Cartridge saves are encrypted per-cartridge.

Without the cartridge, you cannot decrypt the save file.

[Silveraith]

Seems kind of counterproductive to make backups you can't use. I can't picture any greater reason for backing up a cartridge save except for the event that the cartridge becomes inaccessible/unusable. This is terrible. My collection is forever locked behind a door for which the key has been lost.