Well yeah you can always use a different CFW but I highly doubt that's your problem when the one you're using is tried and true. Really seems like a bad SD card to me...... especially since they install fine on your other DS, I doubt you're using the same SD card for both.
SD cards tend to get corrupted sectors fairly easily because people NEVER eject them, they just pull them right out of the PC which is the equivalent to removing a game while it's saving. So do that enough and eventually it will stop being readable entirely.
Well I'm a fan of ejecting and not pulling out...(LoL)
It is the same card- that's why I was so confused! I literally pulled it out of 3ds, reformatted w/ guiformat and started fresh on the n3ds - Installed a9lh and everything and pulled nand backups out of it and everything.
I loaded up from that other eshop just fine too...but as soon as I put on stuff from the pc->msd FBI rejected them.
I decided to try going back to 11.2 and when hourglass9 said my nand backup is corrupted - in nearly fainted! I copied my nand backup off this msd earlier to pc and when I put it on a different msd it thankfully passed the sha check and installed, however, going back to 11.2 didn't fix anything. Turns out the cias I sourced were ok but file integrity was lost during transfer to msd from pc.
I grabbed my Wii U 128gb msd and loaded it up. So far so good! Installs are going through now!
I ran the old msd through that recommended program from 3ds.guide to check card integrity and it errors out after ~1700mb of testing, twice. So into the trash it goes!
And to be honest my msd reader has been acting up and randomly disconnecting without me touching it. In retrospect it was causing disconnections during writes and likely killed the card.
Hopefully my experience here will help others down the line! Thanks for all help!