Not a specific answer, but I can't comment and thought this may be helpful enough to share.

I struggled with this exact issue for a week before finally figuring out that the file I wanted to apply inverse.transform to MUST match the original 'scaled' file regarding the number of columns. In your case above, (26768,29) (31,) (26768,29) is telling you that they aren't the same. In this case, it looks like one file is 29 columns wide while the other is '' wide. Fix that (I dropped a column that had been added between the two events) and you should be good to go.