After clicking submit, I got an error message from Kleki with the option of backing up the file as a .PSD. Can I upload the .PSD somewhere and re-submit somehow? Or does this mean the work is effectively unpostable?

I know you can get the png by uploading it onto Kleki.com and going from there but idk otherwise. :(

You'd have to contact the admin to see if you can get that onto 2draw.

Outside of 2draw, you can open this PSD file in most art software (kleki.com, krita, photoshop, procreate, clip studio) and it will have all your layers. So at least you can continue working on it.