[Ndoki Hasaki]

A computer will not reformat it, it won't even recognize it. There is a way to erase it on computer but it requires command line instructions, and I don't remember how it's done.
Disclaimer - there are so many PC OS's out there now, this may not be accurate for all of them.

I was hoping if I could force a computer to recognize it I could at least back it up before wiping it in case a solution is found in the future.

[Wezard]

If it was formatted as internal, the data is toast, unless you can get it back by reloading the OS while the card is installed. And thats a wild guess.
The FBI or NSA might be able to get it back, or maybe big bucks to a data recovery company.
My disclaimer wasn't that some computers could extract that your data, but that some could erase the card.

[Ndoki Hasaki]

I'm aware that some may be able to erase it, that's not an issue since my phone can do that.

But I find it hard to believe there isn't a way to get a computer to be able to recognize it enough to at least copy the encrypted data as a backup. Especially if one were able to force a computer to recognize the drive, which I have seen programs for.

[Wezard]

Wasn't aware there was an option in the phone to erase the card, you have the option to reformat, but thats not the same thing.
But you can't even do that if the phone doesn't recognize it.
Each phone / card pair has a unique encryption code, generated when you configure it as internal. The same phone will generate a new and different code when a new card is formatted, the old card would no longer be recognized. (Unless you reformatted to external before removing)
You've got a card with heavily encrypted data, and don't have the key. Since you reloaded the OS, the phone no longer has the key.
There prob are some PC programs that will copy the card, it's called cloning, and is mainly for hard drives. But then you have 2 matching pieces of heavily encrypted data and still no key.