5 of 6 added 578 characters in body

Perl 6, 82 bytes

-2 bytes thanks to Jo King

->\n{([-] map {$/=[^n];:10[map {|splice $/,$_,1},[R,] .polymod(1..n-2)]},n+1,n)/9}

Try it online!

0-indexed. Doesn't enumerate all permutations. Should theoretically work for all n, but bails out for n > 65536 with "Too many arguments in flattening array".

The following 80 byte version works for n up to 98!-2 and is a lot faster:

{([-] map {$/=[^99];:10[map {|splice $/,$_,1},[R,] .polymod(1..97)]},$_+1,$_)/9}

Try it online!