Research is needed
Agree with @Dave – a rehearing would be nice, but why publically admit they were wrong in the first place in having a rehearing?
There is a method to get the correct info to SCOTUS, but it does take time, a lot of time, for corrections to be entered, which they enter into the record. See this article: NYT, 5/25/14, SCOTUS keeps editing (https://www.nytimes.com/2014/05/25/us/final-word-on-us-law-isnt-supreme-court-keeps-editing.html)
If Congress really wanted to, they would fund the SCOTUS Research Dept that is needed to ensure correctness is abound.