Terse Method to Swap Lowest for Highest?

How about:

Module[{tmp = test},
    With[{ord=Ordering[tmp]},
        tmp[[ord]] = Reverse @ tmp[[ord]]];
    tmp
]

{56, 9, 4, 3, -5, -2, -3, 1, 2, 7, 60, 58, 8, -4, 10, 6, 59, 5, 57, -1}

This is equivalent to Carl's procedure, except that it uses one less scratch list:

With[{ord = Ordering[test]},
     test[[PermutationProduct[Reverse[ord], InversePermutation[ord]]]]]
   {56, 9, 4, 3, -5, -2, -3, 1, 2, 7, 60, 58, 8, -4, 10, 6, 59, 5, 57, -1}

Recall that list[[perm]] = list is equivalent to list = list[[InversePermutation[perm]]], where perm is a permutation list. (The situation is equivalent to list.pmat being the same as Transpose[pmat].list if pmat is a permutation matrix.) You can then use PermutationProduct[] to compose successive permutations.

(This was supposed to be a comment, but it got too long.)

Permute[Sort @ #, Reverse @ Ordering @ #] & @ test

{56, 9, 4, 3, -5, -2, -3, 1, 2, 7, 60, 58, 8, -4, 10, 6, 59, 5, 57, -1}

Also

Permute[test[[#]], Reverse @ #] & @ Ordering[test]

{56, 9, 4, 3, -5, -2, -3, 1, 2, 7, 60, 58, 8, -4, 10, 6, 59, 5, 57, -1}

and

test[[Reverse @ #]][[Ordering @ #]] & @ Ordering[test] 

{56, 9, 4, 3, -5, -2, -3, 1, 2, 7, 60, 58, 8, -4, 10, 6, 59, 5, 57, -1}